This problem can be done in many ways. I will show 2 ways.

First method.

Case I (both girls sit at the back seat)
No. of ways father or mother can be arranged in driver's seat = 2 ways
No. of ways either of parent and son can be arranged in front seat= 2 ways
No. of ways one girl can be arranged in the first back seat= 2 ways
No. of ways boy can can be arranged in second back seat= 1 way
No. of ways last girl can be arranged in third back seat = 1 way

2*2*2*1*1 = 8

Case II (1 girl sit in the front)
No. of ways father or mother can be arranged in driver's seat = 2 ways
No. of ways either of the girls can be arranged in front seat= 2 ways
1 son, 1 parent & 1 girl can be arranged in back seat = 3! or 6 ways

2*2*6 = 24

24+8=32 ways

Second method

Total number of combinations in which entire family can be arranged
2 for driver's seat
4 for 2 girls, 1 son & either of the parent
remaining can be arranged in 3! or 6 ways at the back.

2*4*3*2*1 = 48 ways

Total number of combinations in which two girls are sitting together =
2 for the driver's seat
2 for either of the parent and son
2! or 2 for girls sitting together at the back
2 for 2 seats left for either the parent or son

2*2*2*2 = 16


48-16 =32

Let me know if you still have any doubts.

Thanx Buddy..its clear now