Call x the number of children.
originally each got $240/x
but later one part was redistributed so each of the (x-1) children got $240/(x-1).
We also know that $240/(x-1) = $240/x + $8. that is our equation to solve for x.
240x = 240*(x-1)+8x(x-1)
240x = 240x - 240 + 8x^2 - 8x
8x^2 - 8x - 240 = 0
this is a quadratic equation with two solutions. you get the solutions using a formula (of your preference). On my end I got the two solutions as x1=-5 and x2=6.
Clearly the solution (number f children) can't be negative, so the one practical solution is x=6 which is the number of children in the Kind family.