Yes, you made an algebraic error. By multiplying 18 x 4, you messed up on order of operations.
(x+9)(x+2)*4
becomes:
(x^2+11x+18)*4
= 4x^2 + 44x + 72
anyway, this is how I would do this problem:
(x+9)(x+2)(4) = 912
(x+9)(x+2) = 228
x^2 + 11x + 18 = 228
x^2 + 11x - 220 = 0
(x+21)(x-10) = 0
x = -21 or 10
The dimensions can't be negative, so we only use x = 10
The dimensions are then 10+9, 10+2, 4
or 19, 12, 4