seating. source: manhattan

MFSD1D2
driver seat can be filled in 2 ways.

Assume Pillion seat is filled by the other parent. this can be done in 1 way
Then, back seats can be filled in only 2 ways (D1SD2 or D2SD1) so that the daughters dont sit together.
All three should happen together. Hence 2*1*2= 4 ways.

Assume Pillion seat is filled by the son. this can be done in 1 way
Then, back seats can be filled in only 2 ways (D1MD2 or D2MD1) so that the daughters dont sit together.
All three should happen together. Hence 2*1*2 = 4 ways.

Assume Pillion seat is filled by the daughter. this can be done in 2 ways.
Then, back seats can be filled in only 3! = 6 ways because there is no restriction.
All three should happen together. Hence 2*2*6 = 24 ways.

Any of these should occur. Hence Add. 4+4+24 = 32 ways.

Hope this helps!!

D-------P

R1 R2 R3

D - driver seat
P - passenger seat
R1 = rear 1
R2 = rear 2
R3 = rear 3

Case 1 :

D can be filled in 2 ways with either parent
P can be filled in 2 ways with either parent not driving or son
R1 can be filled in 2 ways by either sister
R2 has to filled by who ever did not get to sit on P (either son or parent) 1 way
R3 can be filled by left out sister.

total ways in this case = 8

Case 2
D can be filled in 2 ways with either parent
P can be filled in 2 ways with either sister
R1 can be filled in 3 ways by sister who did not get the P seat, son or parent who is not driving
R2 has to filled 2 ways by (sister who did not get the P seat, son or parent who is not driving) -1 as one of these must have sat on R1
R3 can be filled by left out person
total ways in this case = 24

Total overall cases = 24+8 = 32.