Question 310590
As you have assumed, let me assume Sam's father's current age as x years
Then, Sam's current age is 1/6 x = x/6 yrs

After 4 years Sam's age will be x/6 + 4
Sam's dad's age will be (x + 4) years

As per the question:

x/6 + 4 = 1/4 (x + 4)
or, x/6 + 4 = x/4 + 1
or, 4 - 1 = x/4 - x/6
Changing sides:

x/4 - x/6 = 4 - 1
or, (6x - 4x)/24 = 3
or 2x = 3.24
or, x = 36

Therefore Sam is 36/6 = 6 years old