1. **State the problem:** Solve for $x$ in the equation $$-2 \log_4(x) - 10 = -16.$$\n\n2. **Isolate the logarithmic term:** Add 10 to both sides to get $$-2 \log_4(x) = -16 + 10 = -6.$$\n\n3. **Divide both sides by -2:** $$\log_4(x) = \frac{-6}{-2} = 3.$$\n\n4. **Rewrite the logarithmic equation in exponential form:** $$x = 4^3.$$\n\n5. **Evaluate the power:** $$4^3 = 4 \times 4 \times 4 = 64.$$\n\n**Final answer:** $$x = 64.$$