The power radiated by a black body is P and it radiates maximum...

By Stefan's law,
$P = \sigmaA{T}^{4} ⇒ P ∝ {T}^{4}$

According to Wien's law $T ∝ \dfrac{1}{{\lambda}_{m}}$

$⇒ P ∝ {\left(\dfrac{1}{{\lambda}_{m}}\right)}^{4} ⇒ \dfrac{{P}_{2}}{{P}_{1}} = {\left(\dfrac{{\lambda}_{{m}_{1}}}{{\lambda}_{{m}_{2}}}\right)}^{4}$

$⇒ \dfrac{{P}_{2}}{{P}_{1}} = {\left(\dfrac{{\lambda}_{0}}{\dfrac{3}{4}{\lambda}_{0}}\right)}^{4} ⇒ \dfrac{nP}{P} = \dfrac{256}{81} ⇒ n = \dfrac{256}{81}$