let

f = the age of the father now, f>0

s = the age of the son now, s>0

the sum of the ages of a father and son is 46 years

f + s = 46

in 2 yrs, the son will be one-fourth as old as the father

s + 2 = (1/4)(f + 2)

by solving the system of equations

f + s = 46

s + 2 = (1/4)(f + 2)

we find

f = 38 years

s = 8 years

click here to see the step by step solution of the system of equations

the father is 38 years old now.