Rectangle A has length $L$ and width $W - 3$ (3 inches shorter). Rectangle B has length $L$ and width $W$.

$\text{Perimeter of A} = 2L + 2(W - 3) = 2L + 2W - 6$

$\text{Perimeter of B} = 2L + 2W$

$\text{Difference} = (2L + 2W) - (2L + 2W - 6) = 6 \text{ inches}$