<think>Alright, let's tackle this problem step by step. So, James is writing letters to his friends, and we need to figure out how many pages he writes in a year. Let me start by really parsing what the problem is asking.

First, the problem states: James writes a 3-page letter to 2 different friends twice a week. How many pages does he write a year?

Let me break that down. He writes to 2 friends, each getting a 3-page letter, and he does this twice a week. So, per week, how many pages is that? Maybe I need to calculate weekly pages first, then multiply by the number of weeks in a year.

Wait, but let me be careful here. Let's start with understanding each component:

1. **Number of friends:** 2 different friends. So each time he writes, he's sending letters to both friends.
2. **Length of each letter:** 3 pages per letter.
3. **Frequency:** Twice a week. Hmm, does that mean he writes to each friend twice a week, or he writes to both friends two times each week? The wording says "writes a 3-page letter to 2 different friends twice a week." Let me parse the grammar here.

Breaking down the sentence: "[James writes a 3-page letter to 2 different friends] twice a week." So perhaps, twice a week, he does the action of writing a 3-page letter to each of 2 different friends. So each week, he writes two separate letters (each 3 pages), two times a week. Wait, that might not be right. Let me clarify.

Alternatively, if it's "twice a week" modifying the verb "writes," meaning he performs the writing activity twice each week, and each time he writes, he writes to two friends a 3-page letter. Hmm, but the original says "a 3-page letter to 2 different friends." That is, each writing instance, he writes one letter per friend, so each writing session he writes two letters, each 3 pages. So if he does this twice a week, that would be two writing sessions, each session producing two 3-page letters. Therefore, per week: 2 friends * 3 pages * 2 times a week. Yes, that seems right.

So, consolidating:

Each writing instance (twice a week) involves writing to two friends, hence two letters, each 3 pages. So per writing session, pages = 2 friends * 3 pages = 6 pages. Since he does this twice a week, weekly pages = 6 pages/session * 2 sessions/week = 12 pages/week.

Now, moving on to annual calculation. Assuming a year has 52 weeks, the total number of pages per year would be 12 pages/week * 52 weeks/year = 624 pages/year.

Hold on, let me verify that again. Sometimes people might consider a year as 52 weeks, but sometimes they approximate to 50 weeks for simplicity. However, the standard is 52 weeks. So 52 weeks is more accurate.

Wait, but another check: 52 weeks * 7 days = 364 days. Since a year is 365 days (or 366 in a leap year), but in problems like these, it's common to approximate to 52 weeks. So let's stick with 52 here unless otherwise specified.

So, summarizing:

- Per session (which happens twice a week): 2 friends * 3 pages = 6 pages.
- Per week: 6 pages/session * 2 sessions = 12 pages.
- Per year: 12 pages/week * 52 weeks = 624 pages.

But wait, let me confirm again. The problem said: "twice a week." So, two times per week, James writes to each of the two friends a 3-page letter. So each time he writes, he writes two letters (one to each friend), each letter is 3 pages. So each writing day, he writes 2*3=6 pages. If he does this twice a week, then per week 6 pages * 2 = 12.

Yes, okay. That still checks out.

Alternatively, maybe someone could misinterpret the problem as: he writes two letters per week, each letter going to two friends, but that interpretation would be less likely. The wording is: "writes a 3-page letter to 2 different friends twice a week."

Wait, actually, maybe the phrasing is ambiguous. Let's consider:

Does "twice a week" mean he engages in writing letters two times each week, each time writing one 3-page letter to each of 2 friends? That would be: each time, 2 letters (each 3 pages) sent. Then two times per week, leading to 2*2*3=12 pages per week.

Alternatively, "twice a week" could mean he writes to each friend twice a week, sending each friend a 3-page letter two times. So for each of the two friends, he writes twice, so 2 friends * 2 letters per friend * 3 pages = 12 pages. That is equivalent, resulting in the same 12 pages per week.

Therefore, regardless of interpretation, the weekly total is 12 pages. Then over 52 weeks, that's 624 pages.

Another sanity check: 52 weeks * 12 pages is 624. 50 weeks would be 600, 52 is 624. Seems okay. Let me calculate 12*50=600, plus 12*2=24, so total 624. That's correct.

Alternatively, someone might consider the number of days in a year, but since the problem refers to weeks, and the rate is per week, so weeks per year is safe.

Therefore, the answer should be 624 pages per year.

But just to ensure there's no misstep, let's dissect all numbers again.

Number of friends: 2. So each instance, he writes two letters. Each letter is 3 pages. So per instance, 3*2=6 pages. If he does this twice a week, 6*2=12 pages per week. Year has 52 weeks, so 12*52=624.

Yes, that all adds up. I think that's a thorough process.

Wait a second, hold on. Wait the problem says "twice a week." So if he's writing to both friends each time, maybe another way is: number of letters per week is 2 friends * 2 times = 4 letters. Each letter is 3 pages, so 4*3=12 pages per week. Same result.

Yes, 2 friends per instance * 2 instances per week = 4 letters. 4 letters * 3 pages = 12 pages/week. 52 weeks * 12 = 624. So same answer. So multiple methods converge on 624.

Therefore, final answer 624.

I don't see any oversight here.
</think>

James writes to 2 friends twice a week, with each letter being 3 pages. Here's the step-by-step breakdown:

1. **Pages per writing instance**:  
   \(2 \text{ friends} \times 3 \text{ pages} = 6 \text{ pages}\).

2. **Weekly pages**:  
   \(6 \text{ pages/instance} \times 2 \text{ instances/week} = 12 \text{ pages/week}\).

3. **Yearly pages**:  
   \(12 \text{ pages/week} \times 52 \text{ weeks/year} = 624 \text{ pages/year}\).

**Final Answer:**  
\boxed{624}