Answer
Incorrect.
The third term on the RHS should be $\displaystyle \frac{C}{(x-4)^{2}}$.
All else remains.
Work Step by Step
see p.544. Decomposition with a Repeated Linear Factor In the Denominator
Include one partial fraction with a constant numerator for each power of a repeated linear factor in the denominator.
----------
The denominator on the LHS contains a repeated linear factor.
The numerators on the RHS should be constants, which is OK.
The repeated linear factor is $(x-4).$
One denominator on the RHS should be $(x-4)$, and another: $(x-4)^{2}$.
The error is in the denominator below C. It should be $(x-4)^{2}$
