$d_1$ and $d_2$ are equivalent metrics on a set $X$ if and only if there exists a metric space $(Y,\rho)$ and a homeomorphism $h:X\rightarrow Y$

Question

Prove that two metrics $d_1$ and $d_2$ on a set $X$ are equivalent if and only if there exists a metric space $(Y,\rho)$ and a homeomorphism $h:X\rightarrow Y$ from $X$ onto $Y$ such that $d_2(x,y)= \rho (h(x),h(y))$ for $x,y \in X$.

I know the basic definitions and properties of homeomorphism and equivalent metrics, but I am blank on this. Any idea on how to proceed?