Answer: B. $a=\dfrac{x}{8(b+6)}$

Explanation:1. Start with the given equation: $x = 8a(b+6)$

2. Isolate 'a': Our goal is to get 'a' by itself on one side of the equation. The term 'a' is being multiplied by 8 and by $(b+6)$. To isolate 'a', we need to divide both sides of the equation by $8(b+6)$.

3. Perform the division: $\dfrac{x}{8(b+6)} = \dfrac{8a(b+6)}{8(b+6)}$

4. Simplify the equation: On the right side, $8(b+6)$ cancels out from the numerator and denominator: $\dfrac{x}{8(b+6)} = a$

5. Rewrite with 'a' on the left side (optional): $a = \dfrac{x}{8(b+6)}$

6. Compare with the given options: [A] $a=\dfrac{x}{8}-(b+6)$. Incorrect, this involves subtraction rather than division of the entire term. [B] $a=\dfrac{x}{8(b+6)}$. This matches our derived equation. [C] $a=\dfrac{8(b+6)}{x}$. Incorrect, this is the reciprocal of what 'a' should be. [D] $a=8x(b+6)$. Incorrect, this involves multiplying by x instead of dividing.

Conclusion:The equation that correctly expresses a in terms of b and x is $a=\dfrac{x}{8(b+6)}$.