<think>Okay, let me try to figure this out step by step. So, the problem is about Julie reading a 120-page book. We need to find out how many pages she should read tomorrow if she wants to read half of the remaining pages then. Let's see.

Let me break down the problem. First, Julie has a 120-page book. Yesterday, she read 12 pages. Today, she read twice as many pages as yesterday, which would be twice of 12, right? So today she read 24 pages. Then, the remaining pages after yesterday and today would be subtracted from the total, and tomorrow she wants to read half of that remaining portion. The question is asking how many pages she should read tomorrow.

So, summarizing the information given:

- Total pages: 120
- Pages read yesterday: 12
- Pages read today: twice of yesterday, which is 12 * 2 = 24
- Remaining pages after yesterday and today: 120 - 12 - 24 = ?
- Pages to read tomorrow: half of the remaining pages. So, we calculate that number.

Wait, just to make sure I get this right. Let me go step by step.

First, she read 12 pages yesterday. Today, she read twice that amount. So yes, 12*2 = 24. So combined, over the two days, she has read 12 + 24 = 36 pages. The book is 120 pages, so subtracting that from 120 gives us how much is left. 120 - 36 = 84 pages remaining.

Then, she wants to read half of the remaining pages tomorrow. So half of 84 is 84 divided by 2, which is 42. So she should read 42 pages tomorrow.

But let me just verify. Did I do all that correctly? Let me check each step again.

Total book: 120 pages. Correct.

Read yesterday: 12. Correct.

Today: twice as many as yesterday. 12 * 2 = 24. So that's today's reading. Correct.

Total read so far: 12 + 24 = 36. Therefore, remaining pages: 120 - 36 = 84. Alright. Then, half of the remaining is 84 / 2 = 42. That seems right.

Alternatively, maybe there's some wording trick here? Let me re-read the problem.

"Julie is reading a 120-page book. Yesterday, she was able to read 12 pages and today, she read twice as many pages as yesterday. If she wants to read half of the remaining pages tomorrow, how many pages should she read?"

Hmm. So it's about reading half of the remaining pages tomorrow. So "half of the remaining" would be half after subtracting what she's read so far. Since today is the day after yesterday, so if today she's reading, the remaining pages after today would be what's left. Then tomorrow, reading half of that. So the steps are correct. Because after yesterday and today, total pages read: 36. So remaining: 84. Tomorrow's reading: half of that. 42.

But wait, wait a second. The problem says "If she wants to read half of the remaining pages tomorrow." The remaining pages is the total book minus what she's read up to today. So yes, since she's read 12 + 24 = 36, so remaining is 84. So half of that is 42. Therefore, answer is 42.

Alternatively, could the problem have meant "remaining pages after today," which is the same thing. So no trick in the wording. So 42.

Now, let's just make sure that perhaps the order is different. Wait, the problem states: "Yesterday she read 12 pages and today she read twice as many pages as yesterday." So that is correct. Today is the next day after yesterday. So if today she already read twice as many, then remaining pages after today is 84. So tomorrow she’ll read half of 84, which is 42. Yep.

Seems straightforward. Let me check with arithmetic.

Total pages: 120

Read yesterday: 12

Read today: 24 (12*2)

Total read: 12 + 24 = 36

Remaining: 120 - 36 = 84

Half of remaining: 84 / 2 = 42

So tomorrow she should read 42 pages.

Looks good. I think that's right. Not sure if there's any other interpretation. If the problem said, for instance, she wants to read half of the remaining pages each day starting tomorrow, but it's just for tomorrow. So the answer is 42.
</think>

1. **Understanding the Problem**:  
   Julie has a 120-page book. She read 12 pages yesterday and 24 pages today (twice yesterday's amount). We need to find how many pages she should read tomorrow if she wants to cover half of the **remaining** pages after today.  

2. **Breaking Down the Parts**:  
   - Total pages: 120  
   - Pages read yesterday: 12  
   - Pages read today: \( 12 \times 2 = 24 \)  
   - Total read so far: \( 12 + 24 = 36 \)  
   - Remaining pages: \( 120 - 36 = 84 \)  
   - Tomorrow’s goal: \( \frac{84}{2} = 42 \)  

3. **Verification**:  
   Confirming calculations step by step ensures accuracy. The final answer satisfies the condition of reading half the remaining pages.  

**Final Answer**:  
\(\boxed{42}\)