According to the formula:

$$M = m/MV$$

where:

- M is the molarity of the solution (in mol/L)

- m is the mass of the solute (in g)

- V is the volume of the solution (in L)

Let's solve the equation for m:

$$m = MV$$

$$m = (0.4 \text{ mol/L})(500 \text{ mL})$$

$$m = (0.4 \text{ mol/L})(0.5 \text{ L})$$

$$m = 0.2 \text{ mol}$$

Finally, we convert moles to grams:

$$m = (0.2 \text{ mol})(40 \text{ g/mol})$$

$$m = 8 \text{ g}$$

Therefore, 8 grams of solid NaOH are needed to prepare 500mL of a 0.4M solution.