According to law of equivalence,

Equivalence of acid = Equivalence of base.

Equivalence of acid = Normality x volume = 0.1 $$ \times $$ v

As we know base produce OH^$$-$$ ion, so moles of base is same as moles of OH^$$-$$ ion = 0.04

Another formula of equivalence = n factor $$ \times $$ number of moles

$$\therefore\,\,\,$$ Equivalance of base = n factor of OH^$$-$$ $$ \times $$ moles of OH^$$-$$ = 1 $$ \times $$ 0.04

As for any ion, the charge of that ion is the n factor of that ion. Here OH^$$-$$ has 1 negative charge so it's n factor = 1

$$\therefore\,\,\,$$ 0.1 $$ \times $$ v = 1 $$ \times $$ 0.04

$$ \Rightarrow $$$$\,\,\,$$ v = 0.4 L

=   0.4 $$ \times $$ 1000

=    400 ml.