jmc

The rhombus is split into four congruent right triangles. Each right triangle has a leg of $\frac{6}{2}=3$ inches and another leg of $\frac{8}{2}=4$ inches. We use the Pythagorean Theorem to solve for the length of the hypotenuse, or we recognize that $3$ and $4$ are part of the Pythagorean triple $(3,4,5)$, so the length of the hypotenuse is $5$ inches. Each side of the rhombus is $5$ inches long, so the perimeter is $4(5)=\boxed{20}$ inches.