Work done in rearranging the four charges from configuration (1) to configuration (2) is

Configuration (1): charges at four corners.

Side pairs (4):

$$4\cdot\frac{kq_0^2}{a}$$

Diagonal pairs (2):

$$2\cdot\frac{kq_0^2}{a\sqrt{2}}$$

So,

$$U_1=\frac{kq_0^2}{a}(4+\sqrt{2})$$

Configuration (2): charges at midpoints of four sides.

Distance between adjacent midpoints:

$$\frac{a}{\sqrt{2}}$$

4 such pairs:

$$4\cdot\frac{kq_0^2}{a/\sqrt{2}}=\frac{4\sqrt{2}kq_0^2}{a}$$

Distance between opposite midpoints:

a

2 such pairs:

$$2\cdot\frac{kq_0^2}{a}$$

Thus,

$$U_2=\frac{kq_0^2}{a}(4\sqrt{2}+2)$$

Work required:

$$W=U_2-U_1$$

$$=\frac{kq_0^2}{a}(3\sqrt{2}-2)$$