Frequency of unknown tuning fork may be ${n_B} = 256 + 4 = 260\,Hz$ 

or $ = 256 - 4 = 252\,Hz$

It is given that on sounding waxed fork $A$ (fork of frequency $256 Hz$) and fork $B$, number of beats (beat frequency) increases. 

It means that with decrease in frequency of $A,$ the difference in new frequency of $A$ and the frequency of $B$ has increased.

This is possible only when the frequency of $A$ while decreasing is moving away from the frequency of $B.$

This is possible only if $n_B = 260 Hz.$

Alternate method : It is given ${n_A} = 256\,Hz,\,{n_B} = ?$ and $x = 4 \,bps$ 

Also after loading $A$ (i.e. $n_A \downarrow$), beat frequency (i.e. $x$) increases ($\uparrow$).

Apply these informations in two possibilities to known the frequency of unknown tuning fork. 

$n_A \downarrow -n_B = x\uparrow$ ... $(i)$

$n_B -n_A \downarrow = x\uparrow$ ... $(ii)$

It is obvious that equation $(i)$ is wrong $(ii)$ is correct so 

$n_B = n_A + x = 256 + 4 = 260 \,Hz.$