1. **State the problem:** Solve the equation $2(2+m)=16$ for $m$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses. $$2 \times 2 + 2 \times m = 16$$ 3. **Simplify:** $$4 + 2m = 16$$ 4. **Isolate the term with $m$:** Subtract 4 from both sides. $$4 + 2m - \cancel{4} = 16 - \cancel{4}$$ $$2m = 12$$ 5. **Solve for $m$:** Divide both sides by 2. $$\frac{2m}{\cancel{2}} = \frac{12}{\cancel{2}}$$ $$m = 6$$ 6. **Final answer:** $m=6$