1. **State the problem:** Given the equation $$4\sqrt{2x} = 16$$, find the value of $$6x$$. 2. **Write the formula and rules:** We need to isolate $$x$$ by solving the equation. Recall that $$\sqrt{a}$$ means $$a^{\frac{1}{2}}$$. 3. **Isolate the square root term:** Divide both sides by 4: $$\frac{4\sqrt{2x}}{4} = \frac{16}{4}$$ $$\cancel{4}\sqrt{2x} = \cancel{4}4$$ $$\sqrt{2x} = 4$$ 4. **Square both sides to remove the square root:** $$\left(\sqrt{2x}\right)^2 = 4^2$$ $$2x = 16$$ 5. **Solve for $$x$$:** $$x = \frac{16}{2}$$ $$x = 8$$ 6. **Find $$6x$$:** $$6x = 6 \times 8 = 48$$ **Final answer:** $$6x = 48$$, which corresponds to choice B.