Close, but not quite right.
If you let x represent the measure of angle C, then, as you have, the measure of angle B is 3x+2.
The sum of angles B and C is 90, so the setup is ...
... (3x+2) +(x) = 90
... 4x = 88 . . . . . . . . . . collect terms, subtract 2
... x = 22 = m∠C
... 3x+2 = 68 = m∠B
