let the present age of Ajay is $2x$ and Vijay present age is $3x$.
It is given that Ajay is $6$ year younger than Vijay: $2x=3x-6\implies x=6$
such a present age of Ajay=$12$ year
present age of Vijay=$18$
So the ratio of Ajay to Vijay age after $6$ year $=\frac{12+6}{18+6}\implies\frac{18}{24}=\frac{3}{4}$
So Option $(D)$ is correct.