1. The problem is to calculate $4^2$. 2. The expression $4^2$ means 4 raised to the power of 2, which is the same as multiplying 4 by itself. 3. The formula for exponentiation is $a^b = a \times a \times \cdots \times a$ ($b$ times). 4. Applying this, $4^2 = 4 \times 4$. 5. Multiplying, $4 \times 4 = 16$. 6. Therefore, the final answer is $16$.