Answer
True.
Work Step by Step
Area of a circle with radius of 2 inches:
$A=\pi2^2=4\pi~in^2$
Area of a square with a side length of 4 inches.
$A=l^2=4^2=16~in^2$
We know that $\pi=3.14...$ So:
$\pi\lt4$
$4\pi\lt4\times4$
$4\pi\lt16$