Make this chart


               number        time        filling
              of tanks     required      rate in
               filled      in hours      tanks/hr
pipe A alone
pipe B alone
both togther

and since we are talking only about filling ONE tank, we put
1 for the number of tanks filled in all three cases:

               number        time        filling
              of tanks     required      rate in
               filled      in hours      tanks/hr
pipe A alone      1
pipe B alone      1
both togther      1


We are asked how long it will take each pipe alone to fill ONE tank.

Let x = number of hours it will take pipe B alone to fill ONE tank.

So x+6 = number of hours it will take pipe A alone to fill the tank.


               number        time        filling
              of tanks     required      rate in
               filled      in hours      tanks/hr
pipe A alone      1          x+6
pipe B alone      1           x
both togther      1

So fill in 4 for the time reequired for both together:

               number        time        filling
              of tanks     required      rate in
               filled      in hours      tanks/hr
pipe A alone      1          x+6
pipe B alone      1           x
both togther      1           4

Now fill in the three rates in tanks/hr by dividing
the number of tanks by the hours:

               number        time        filling
              of tanks     required      rate in
               filled      in hours      tanks/hr
pipe A alone      1          x+6         1/(x+6)
pipe B alone      1           x            1/x
both togther      1           4            1/4

The equation comes from



So the equation is

 

To solve that you clear of fractions and simplify to
a quadratic equation.  Then you get two solutions and
discard the negative one and get

x = 6, which is how many hours it would take pipe B

And we add 6 to that,

x+6 = 12, which is how many hours it would take pipe A

Edwin