Currently, I am 9 times as old as my son. Next year, I will be 6 times as old as my son. How old is my son now?

Let your the current age of your son = N

Then your current age = 9N

And in one year we have this relationship

9N + 1 = 6 ( N + 1) simplify

9N + 1 = 6N + 6

9N - 6N = 6 - 1

3N = 5

N = 5/3 = 1 + 2/3 yrs old = 1yr and 8 months old = your son's age now

The son is 1-2/3 years old.

9 times 1-2/3 years is 15 years, i.e., the father's age now.

But the son is over a year old now, which means

the father was at most 14 when his son was born.