When Nabil's age was same as Shuvo's present age, at that time Nabil's age was twice as Shuvo's age. When Shuvo's age will be same as Nabil's present age, the sum of their ages will be 63. What is the present age of each of them?

Shuvo's present age = $S$
Nabil's present age = $N$
Present $\leftrightarrow Y=0$ ("year 0")

"When Nabil's age was same as Shuvo's present age" $\leftrightarrow Y = Y_1$
$N+Y_1 = S$
"At that time Nabil's age was twice as Shuvo's age"
$N+Y_1 = 2(S+Y_1)$

"When Shuvo's age will be same as Nabil's present age" $\leftrightarrow Y = Y_2$
$S+Y_2 = N$
"Sum of there age will be 63"
$(S+Y_2) + (N+Y_2) = 63$

Based on the wording, we expect $Y_1 < 0$ (in the past) and $Y_2 > 0$ (in the future).

Four equations, four unknowns ($S, N, Y_1, Y_2$), you should be able to find them all.

*whispers* (What happened to not giving them the answers but helping them with the tools to find the answers on their own, and then once they had a reliable grasp on the fundamentals, telling them, "By the way, if you notice in this case, there is a shortcut you could take...?")