The potential barrier existing across an unbiased p - n junction is...

The potential barrier across the $p$-$n$ junction is given as $V = 0.2 \text{ V}$.

The $n$-side of the junction is at a higher potential than the $p$-side by $0.2 \text{ V}$.

For a hole (charge $q = +e$) to diffuse from the $p$-side to the $n$-side, it must overcome this potential barrier.

The minimum kinetic energy required by the hole is equal to the potential energy barrier it needs to cross.

K_{\text\min} = qV

K_{\text\min} = e \times 0.2 \text{ V} = 0.2 \text{ eV}