Answer: B. x: -6,0,6,12; f(x): 12,24,48,96

Explanation:1. Evaluate the function $f(x)=24(2)^{\dfrac{x}{6}}$ for each of the common x-values used in the tables: $-6, 0, 6, 12$.

2. Calculate $f(-6)$: $f(-6) = 24(2)^{\dfrac{-6}{6}} = 24(2)^{-1}$ Since $2^{-1} = \dfrac{1}{2}$, $f(-6) = 24 \times \dfrac{1}{2} = 12$.

3. Calculate $f(0)$: $f(0) = 24(2)^{\dfrac{0}{6}} = 24(2)^0$ Since $2^0 = 1$, $f(0) = 24 \times 1 = 24$.

4. Calculate $f(6)$: $f(6) = 24(2)^{\dfrac{6}{6}} = 24(2)^1$ $f(6) = 24 \times 2 = 48$.

5. Calculate $f(12)$: $f(12) = 24(2)^{\dfrac{12}{6}} = 24(2)^2$ Since $2^2 = 4$, $f(12) = 24 \times 4 = 96$.

6. Compare these calculated values with the values in each option's table: We are looking for the table with: x = -6, f(x) = 12 x = 0, f(x) = 24 x = 6, f(x) = 48 x = 12, f(x) = 96

[A] x: -6,0,6,12; f(x): 12,$0$,48,96 (Incorrect, $f(0)$ is $24$, not $0$) [B] x: -6,0,6,12; f(x): 12,24,48,96 (This matches all our calculated values) [C] x: -6,0,6,12; f(x): $-12$,24,48,96 (Incorrect, $f(-6)$ is $12$, not $-12$) [D] x: -6,0,6,12; f(x): 12,24,48,$72$ (Incorrect, $f(12)$ is $96$, not $72$)

7. Identify the correct table: Table [B] matches all calculated values.

8. Conclusion: The table that gives four correct values of x and their corresponding values of $f(x)$ for the given exponential function is option [B].