Correct Answer - Option 4 : sin(ππ/6)/(ππ)
\(x\left[ n \right] = \frac{{\sin \left( {\frac{{n\pi }}{6}} \right)}}{{n\pi }}\)
\(h\left[ n \right] = \frac{{\sin \left( {{\omega _c}n} \right)}}{\pi },{\omega _c} > \frac{\pi }{6}\)
output, y[n] = x[n] * h[n]
in frequency domain both will get multiplied
\(y\left[ n \right] = \frac{{\sin \left( {\frac{{n\pi }}{6}} \right)}}{{n\pi }}.\frac{{\sin \left( {{\omega _c}n} \right)}}{\pi }\)
\(= \frac{{\sin \left( {\frac{{n\pi }}{6}} \right)}}{{n\pi }}\;as\;{\omega _c} > \frac{\pi }{6}\)