Two pipes A and B together can fill a tank in $4$ hours. Pipe B take $6$ hours more than A to fill the tank, if they are opened separately. The time taken by A to fill the tank alone is

Suppose pipe A alone fill cistern in x hours. So, pipe B fill the cistern in $(x+6)$ hours.

Thus, from the given problem is,

$\begin{array}{l}\frac{1}{x}+\frac{1}{(x+6)}=\frac{1}{4}\\ \Rightarrow \frac{x+6+x}{x(x+6)}=\frac{1}{4}\\ \Rightarrow x^2-2x-24=0\\ \Rightarrow (x-6)(x+4)=0\end{array}$

Neglect the negative value,

$\Rightarrow x=6$