$H =\frac{ V ^{2}}{ R } t$  $....(i)$

It is given $20 \%$ heat is heat to be ejected, thus, the resistance is reduced by $20 \%$

The new resistance is,

$R ^{\prime}= R -0.2 R =0.8 R$

The new amount of heat generated is,

$H ^{\prime}=\frac{ V ^{2}}{0.8 R } t ^{\prime}$ $....(ii)$

On equating both equations $(i)$ and $(ii)$ we get,

$\frac{ V ^{2}}{ R } t =\frac{ V ^{2}}{0.8 R } t ^{\prime}$

$t ^{\prime}=0.8 \times t =0.8 \times 12 min =9.6 min$