4 grams of a metal on heating with $O_2$, gave $4.5$ grams of the metal oxide. The equivalent weight of the metal is

$4 g$ of metal produce $4.5 g$ of metal oxide, thus amount of oxygen present in $4.5 g$ of metal oxide is $4.5-4=0.5 g$

As it is known that 

$Mass of metal/mass of O_2 = eq. weight of metal/eq. weight of O_2$

$Eq. weight = atomic weight/valency$

-Therefore, mass of metal $=4 g$, mass of oxygen $=0.5 g$, eq. weight of oxygen is $\frac{16}{2}=8$ and need to find eq. weight of metal

-By substituting the values in formula, we get $\frac{4}{0.5}=\frac{X}{8}$

$X=\frac{4}{0.5}X8=8\times 8=64$

Equivalent weight of metal is$64$

Hence the correct option is D.