The volume of rectangular solid $\mathrm{A}$ is equal to the volume of rectangular solid $\mathrm{B}$. If the length of solid A is three times the length of solid B, and the height of solid $\mathrm{A}$ is twice the height of solid $B$, then

The volume of a rectangular solid is equal to $lwh$, where $l$ is the length of the solid, $w$ is the width of the solid, and $h$ is the height of the solid. If $l$ is the length of solid B and $h$ is the height of solid $B$, then the length of solid $A$ is $3l$ and the height of solid $\mathrm{A}$ is $2h$. Since the volumes of the solids are equal, if $w_1$ represents the width of solid $\mathrm{A}$ and $w_2$ represents the width of solid B, then $(3l)(2h)\left(w_1\right)=(l)(h)\left(w_2\right),6w_1=w_2$, which means that $w_2$, the width of solid $\mathrm{B}$, is equal to 6 times the width of solid $A$.