Assume the present age of the father is $x$ year, son's age is $y$ year.
$4$ year ago father age=$(x-4)$
$4$ year ago son age =$(y-4)$
now it is give that: father's age=6(son’s age)
$\therefore (x-4)=6(y-4)$
$\implies x-4=6y-24$
$\implies x-6y=-20 ------ (i)$
Now after $16$ year father’s age =$(x+16)$
son’s age after $16$ year= $(y+16)$
now it is given that father age=2(son’s age)
$\implies (x+16)=2(y+16)$
$\implies x+16=2y+32$
$\implies x-2y=16------ (ii)$
from equation $(i) \& (ii)$ we get son’s age $y=9$ year, father’s age $x=34$ year.
Option (A) is correct.