1. **Problem statement:** Find the number of ways 4 boys and 4 girls can sit at a square table with two seats on each side such that each side has exactly one boy and one girl. 2. **Understanding the problem:** The table has 4 sides, each with 2 seats. Each side must have 1 boy and 1 girl. 3. **Step 1: Arrange boys** - There are 4 boys and 4 sides. - Assign one boy to each side. - Number of ways to arrange boys on 4 sides is $4! = 24$. 4. **Step 2: Arrange girls** - Each side has 1 remaining seat for a girl. - We must place 4 girls, one on each side. - Number of ways to arrange girls is $4! = 24$. 5. **Step 3: Seating order on each side** - Each side has 2 seats: one for a boy and one for a girl. - The boy and girl can switch seats on their side. - For each side, 2 ways to arrange boy and girl. - For 4 sides, total ways = $2^4 = 16$. 6. **Step 4: Calculate total arrangements** - Multiply all possibilities: $$4! \times 4! \times 2^4 = 24 \times 24 \times 16 = 9216$$ 7. **Final answer:** There are **9216** ways for 4 boys and 4 girls to sit at the square table with the given conditions.