My car drives just fine. However, it will not reverse. The grears slip, they won't catch for reverse or park. My machanic says it's some box in the steering coloum, but I want to be sure. What do you think and how much is it

If you doubt your mechanic, first I would say find a new mechanic, if you don't have one you trust completely, like a doctor, find one you will feel good about.

No matter how good a mechanic can be wrong sometimes.

And like a doctor, get a second opinion, take it to another shop to see if they agree.