Let $H$ and $K$ be subgroup of a group $G$ and $a$,$b$ $\in$ $G$ Then if $aH$$\subseteq$$bK$ then $b^{-1}aH$$\subseteq$$K$

I don’t know how to do this , can we just pre multiple both side by $b^{-1}$ ? Even if we can do this I am still not able to picture this step in my head.
I know some basic properties of cosets like if $aH$=$bH$ then $a^{-1}b$$\in$$H$ .

Please help to get picture of this rule.