To solve a congruence with modulus 63 by the CRT, you need to solve it mod 9 (not 3) and mod 7. But in cases like this, it's often quicker to cancel by a common factor first.
The congruence is equivalent to . The reason for this is that if 15x+12=63k then you can divide by the common factor 3 to get 5x+4=21k.
The congruence has the solution x=5, and you get the solutions to the original congruence by adding multiples of 21.