When I turn my AC unit on, the front right mat in my car gets soaked.

First I just wanted to Thank you very much for your answer. I have 1 more question for you. Is there a way I can buy the part & put it in myself. Because I have money problems. Or if I can't do you know if it will cost me a lot of money to have it fixed. Just wanted to Thank You for your answer in the first place. Twiggy50

Fairly easy and cheap repair. All shops can perform service at a reasonable price. Here's one DIY technique : https://www.youtube.com/watch?v=c3OipaWX3_Q