Answer: D. $32$

Explanation:1. Analyze the given equation: $\dfrac{x-16}{18}=\dfrac{x-16}{9}$ One way for this equation to be true is if the numerator $x-16$ is equal to $0$. If $x-16 = 0$, then $x=16$. In this case, the equation becomes $\dfrac{0}{18} = \dfrac{0}{9}$, which simplifies to $0=0$. This is true. So, $x=16$ is a solution.

2. Alternative approach: Solve algebraically. Let $A = x-16$. The equation becomes $\dfrac{A}{18} = \dfrac{A}{9}$. Multiply both sides by $18$ to clear denominators: $18 \times \dfrac{A}{18} = 18 \times \dfrac{A}{9}$ $A = 2A$ Subtract A from both sides: $0 = 2A - A$ $0 = A$ Since $A = x-16$, we have: $x-16 = 0$ $x = 16$

3. Calculate the value of $x+16$: We found that $x=16$. The question asks for the value of $x+16$. $x+16 = 16+16 = 32$.

4. Check the solution with the options: The value of $x+16$ is $32$. This matches option [D].

5. Conclusion: The value of $x+16$ is $32$.