1. **State the problem:** Simplify and solve the expression $$\frac{1}{2} \left[ 8x + 10 - 6 \left( 1 - 4x \right) \right]$$. 2. **Apply the distributive property inside the brackets:** $$8x + 10 - 6(1 - 4x) = 8x + 10 - 6 + 24x$$ 3. **Combine like terms inside the brackets:** $$8x + 24x + 10 - 6 = 32x + 4$$ 4. **Multiply by $ \frac{1}{2} $:** $$\frac{1}{2} (32x + 4) = \frac{1}{2} \times 32x + \frac{1}{2} \times 4 = 16x + 2$$ 5. **Final simplified expression:** $$16x + 2$$ This is the simplified form of the given expression. Since no equation is given (no equals sign), this is the final answer.