According to Wien's displacement law, the wavelength corresponding to maximum spectral emissive power is inversely proportional to the absolute temperature of the black body, i.e., $\lambda_m T = \text{constant}$. Given initial wavelength $\lambda_1 = \lambda_0$ at temperature $T_1$, and final wavelength $\lambda_2 = \frac{3}{4}\lambda_0$ at temperature $T_2$. Therefore, $\lambda_0 T_1 = \frac{3}{4}\lambda_0 T_2 \implies T_2 = \frac{4}{3}T_1$. According to the Stefan-Boltzmann law, the total power radiated by a black body is directly proportional to the fourth power of its absolute temperature ($P \propto T^4$). So, the ratio of final power to initial power is $\frac{P_2}{P_1} = \left(\frac{T_2}{T_1}\right)^4 = \left(\frac{4}{3}\right)^4 = \frac{256}{81}$. Given $P_1 = P$ and $P_2 = nP$, we have $\frac{nP}{P} = \frac{256}{81} \implies n = \frac{256}{81}$.