A car has an initial velocity of 20 m/s to the right, 17 seconds later it is seen to be moving at 46 m/s to the left.

WHAT DISTANCE DID IT TRAVEL?

Does the 17 seconds include the initial 20m/s? If not, how do I find the other distance. If so... What do I do. Sorry I am in a pickle.

A very stupid problem. Assume your instructor meant:

A car passing a certian point is traveling 17m/s to the right. 17 seconds later, at some point it is going 46m/s to the left. Assume the car is under constant acceleration at all times.

Vf=vi+at
-46=17 + a*17
solve for acceleration. It will be negative ...then
distannce=vi*t+1/2 a 17^2 using the a from above. Notice I used + for right, - for left direction.