Calculating the Number of Possible Arrangements:
To solve this problem, we can use the concept of permutations.

Step 1: Total Number of Arrangements
- Let's start by calculating the total number of arrangements when all 4 children are seated without any restrictions.
- Since there are 4 children, the total number of arrangements will be 4! = 24.

Step 2: Calculating the Number of Arrangements with Girls Seated Together
- We need to calculate the number of arrangements where the girls are seated together.
- Since there are 2 girls, we can treat them as a single entity. So, we have 3 entities to arrange (2 girls and 2 boys).
- The number of arrangements with girls seated together is 3! = 6.
- However, since there are 2 ways to arrange the girls within this group (Girl 1 - Girl 2 or Girl 2 - Girl 1), we need to multiply by 2. So, the total number of arrangements with girls seated together is 6 * 2 = 12.

Step 3: Calculating the Number of Arrangements with Girls Not Seated Together
- To find the number of arrangements where the girls are not seated together, we need to subtract the number of arrangements with girls seated together from the total number of arrangements.
- Number of arrangements with girls not seated together = Total number of arrangements - Number of arrangements with girls seated together
- Number of arrangements with girls not seated together = 24 - 12 = 12.

Final Answer:
- Therefore, there are 12 possible arrangements where 2 boys and 2 girls are seated in a row such that the girls are not next to each other.