Question 521371
Let 
Present age of Father = f
Present age of Daughter = d

4 years ago
Age of father  = f-4
Age of daughter = d-4
Then
The father was 8 times older than his daughter
f-4=8(d-4)
f-4=8d-32
f=8d-32+4
f=8d-28......................(1)


In twenty years time 
Age of father will be = f + 20
Age of daughter will be = d+ 20
Then
father will be twice the age of the daughter. 
f+20=2(d+20)
f+20=2d+40
f=2d+40-20
f=2d+20.......................(2)


Plug in the value of f from (1) to (2)
8d-28=2d+20
8d-2d=20+28
6d=48
6d/6=48/6
d=8
Put the value of d in (1)
f=8d-28
f=8(8)-28
f=64-28
f=36



Present age of Father = f = 36 years old
Present age of Daughter = d = 8 years old
Daughter will be 38 years old after 30 years.