<think>Okay, let's see. So the problem is about Julie reading a 120-page book. Let me try to break it down step by step. Yesterday she read 12 pages, and today she read twice as many as yesterday. Then she wants to read half of the remaining pages tomorrow. The question is, how many pages should she read tomorrow? 

First, I need to visualize this. The book is 120 pages total. Yesterday, she read 12 pages. Today, she read twice as many as yesterday. Twice of 12 is 24, right? So today she read 24 pages. So far, in total, she's read 12 + 24 pages. Let me confirm that. 12 plus 24 is 36 pages. So she has already read 36 pages. 

Now, the total book is 120 pages. If she has read 36 pages so far, the remaining pages would be 120 minus 36. Let me calculate that. 120 minus 36 is 84. So there are 84 pages left after today. 

But the problem states she wants to read half of the remaining pages tomorrow. So half of 84 is... let me divide 84 by 2. 84 divided by 2 is 42. Therefore, she needs to read 42 pages tomorrow.

Wait, let me check if I did that right. Let me go through each step again to verify. 

Starting pages: 120. Yesterday’s reading: 12. Today’s reading: twice that, so 12x2=24. Total read so far: 12+24=36.

Remaining pages: 120-36=84. Half of remaining: 84/2=42. So yes, 42 pages. That seems correct. 

But hold on, maybe make sure "remaining pages" is after today. So after today, how many pages are left? Yes, after yesterday and today, total read is 12 + 24. Total pages read: 36. Thus remaining is 120-36=84. Therefore, half of that is indeed 42.

So yeah, the answer should be 42 pages. Let me just check once more. Total book: 120. First day (yesterday):12. Second day (today): 24. Total two days:36. Left: 84. Tomorrow, half left:42. That’s under 84, so 42 makes sense. Yes, 42 seems right. They want the number of pages she should read tomorrow, which is 42. Alright, feel confident now.
</think>

Julie needs to read **42 pages** tomorrow.  

**Step-by-Step Explanation:**  
1. **Total Pages:** 120 pages  
2. **Pages Read Yesterday:** 12 pages  
3. **Pages Read Today:** \( 12 \times 2 = 24 \) pages (twice as many as yesterday)  
4. **Total Pages Read So Far:** \( 12 + 24 = 36 \) pages  
5. **Remaining Pages After Today:** \( 120 - 36 = 84 \) pages  
6. **Pages to Read Tomorrow (Half of Remaining):** \( \frac{84}{2} = 42 \) pages  

**Answer:**  
\boxed{42}