The gravitational force between two objects is $F$. If masses of both objects are halved without changing distance between them, then the gravitational force would become
$(a).\ F/4$
$(b).\ F/2$
$(c).\ F$
$(d).\ 2F$

As known that the force of attraction between the two objects is inversely proportional to the square of the distance between the two objects.

So, $F=G\frac{m_1m_2}{r^2}$

Here, $F\rightarrow$ force of attraction between the two objects.

$r\rightarrow$ distance between the two objects.  

$m_1$ & $m_2\rightarrow$ masses of the two objects

If the masses of both the two objects are halved, then they will become $\frac{m_1}{2}$ and $\frac{m_2}{2}$.

Then, force of attraction, $F'=G\frac{\frac{m_1}{2}\times \frac{m_2}{2}}{r^2}$

Or $F'=\frac{1}{4}(G\frac{m_1m_2}{r^2})$

Or $F'=\frac{1}{4}\times F$

So, option $(a)$ is correct.