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