How do you add two vectors?

Do you mean concatenate?

let mut a = vec!['a', 'b', 'c'];
let mut b = vec!['d', 'e', 'f'];

b.append(&mut a);

assert!( b == vec!['a', 'b', 'c', 'd', 'e', 'f'] );

Append will move all items from one vector to the end of the other.

This question from several years ago covers some other ways, depending on what you need the state of the original vectors to be afterwards.