Explanation

(b) Wavelength of radiation $\lambda_{1} = 12000\mathring{\mathrm{A}}$
Temperature of star $T_{1} = 2600\ K$
Wavelength of star spectrum $\lambda_{2} = 5000\mathring{\mathrm{A}}$
Temperature of star $T_{2} = ?$
From Wien law
$\lambda_{1}T_{1} = \lambda_{2}T_{2}$
$T_{2} = \ \frac{\lambda_{1}T_{1}}{\lambda_{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \frac{12000 \times 2600}{5000}$
$T_{2} = 6240\ K$