For (1) I presume you were able to calculate that, since the car "accelerates to 11m/s in 4.0s.", the (average) acceleration is a= 11/4 m/s^2. Since the car "starts from rest", v0= 0 and since it starts "at x0= 6.2m", x0= 6.2. So using your "x = x0 + v0t + 1/2at^2", x= 6.2+ (11/8)t^2. With t= 4s that is x= 6.2+ (11/8)(16)= 6.2+ 22= 28.2 m.
I have absolutely no idea how you got "88". Could you show us your working?
For (2), "How much time does it take to an object to accelerate from 10.0m/s to 15m/s while moving from x0=8.0m to x=29m?", taking "t" to be the required time and "a" the (average) acceleration, x= x0+ v0t+ at^2= 8+ 10t+ at^2= 29 while v= v0+ at= 10+ at= 15.
Solve the two equations 8+ 10t+ at^2= 29, so at^2+ 10t 21= 0, and 10+ at= 15, so at= 5, for a and t. I would start by solving the second for a= 5/t so that at^2+ 10 21= 0 becomes (5/t)(t^2)+ 10t 21= 5t+ 10t 21= 0 or 15t= 21.
