When you see these types of problems you want to think of that negative sign (-) as -1*(-4x - 6). So you multiply all of the terms inside by -1. Then you combine like terms.
(11x - 9) - (-4x - 6)
Multiply -4x by -1. And -6 by -1.
11x - 9 + 4x + 6
Combine the like terms. (Like terms are anything with the same number of the same type of variables. So in this case there are two like pairs. One pair has one x. The other pair has 0 x's)
11x + 4x + 6 - 9
15x - 3
That is our answer!