Final answer:
The largest number of groups they can be split into and have the same number of boys and girls on each team is 6.
Step-by-step explanation:
To determine the largest number of groups that can be made with an equal number of boys and girls, we need to find the greatest common divisor of the number of boys and girls. In this case, there are 18 boys and 12 girls. The greatest common divisor of 18 and 12 is 6. So, they can be split into 6 groups with 3 boys and 2 girls in each group.