42 oranges are distributed among some boys and girls. If each boy gets 3, then each girl gets 6. But if each boy gets 6 and each girl gets 3, it needs 6 more. The number of girls is 

Let number of boys is x and number of girls is y 

According to the question,

$3x+6y=42$    …(1)

$6x+3y=42+6$  …(2)

Multiply eqn (1) by 2 and then, subtracting eqn (2) from eqn (1).

$6x+12y=84$  ...(3)

$6x+3y=48$  ...(2)

Subtract eqn (2) and (3)

$\begin{array}{l}9=36\\ =4\end{array}$

Put the value of y in eqn (2) 

$\begin{array}{l}6x+3\times 4=48\\ 6x=48-12\\ 6x=36\\ x=6\end{array}$

So, number of girls is 4.