1. **State the problem:** Simplify the expression $4(a+4b)-2(a+b)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4(a+4b)-2(a+b) = 4a + 16b - 2a - 2b$$ 3. **Combine like terms:** Group the $a$ terms and the $b$ terms. $$4a - 2a + 16b - 2b$$ 4. **Simplify each group:** $$\cancel{4a} - \cancel{2a} = 2a$$ $$16b - 2b = 14b$$ 5. **Write the final simplified expression:** $$2a + 14b$$ This is the simplified form of the original expression.