$\begin{array}{1 1}24J\\22J\\20J\\34J\end{array} $

Answer : 24J

First we need to find the spring constant.Let $x$ denote the distance the spring is stretched beyond its natural length.We know when $x=\large\frac{1}{2}$ we have $F=6$,so it follows that $6=\large\frac{m}{2}$ or $m=12$.Thus the force required to maintain this spring stretched $x$ units beyond its natural length is $f(x) =12x$

Now we need to calculate the work required to stretch it to a length of 6m.Since we are stretching it from its natural length to 6m,we are finding the work done for $0 \leq x \leq 2$.Therefore we have

$W=\int_0^2 12xdx =24J$

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