The father is 60, and the son is half of 60, so the son is 30.
The difference in ages is 60 - 30 = 30.
The difference in ages is 30 years. That difference is always true, no matter how old they are.
When the father was 4 times the age of the son, the son was b years old and the father was 4b years old. The difference in ages is still 30, so that gives us our equation.
4b - b = 30
3b = 30
b = 10
Answer: 10 years old