Digital Signal Analysis: Sinusoid and Filtering problem
The frequency components in \$x(t)\$ are :  DC, 12Hz, 24Hz and 32Hz.

(i) So the signal is going to be repeated at 4Hz. or \$T=0.25sec\$  

(ii) You are taking the IFFT of b to get x. or, b will have non-zero values at zeroth harmonics (DC), 3rd harmonics (12Hz), 6th harmonics (24Hz) and at 8th harmonics (32Hz) of fundamental frequency (4Hz) all other positions will be occupied by zeroes. The non-zero values would be in form \$magnitude\times exp(phase)\$.  Hence the answer.

(iii) You are using an LPF with \$f_c = 15hz\$. Therefore output will contain frequency components less than 15Hz only. 
$$y(t) = 1.7 + 3.5cos(24\pi t - 2.1)$$