That's really strong

The original solution has strength 15% and is 400ml so has $\frac{15}{100} \times 400 = 60$ ml of alcohol. Let x be the volume of pure alcohol added. Then the concentration is $\frac{60 + x}{400+x}$ which equals $\frac{32}{100}$ .

Rearranging this we get:

$60+x = \frac{32}{100} (400+x)$

$60+x = 128 + \frac{32}{100} x$

$\frac{68}{100} x = 68$

$x = \boxed{100}$