The correct options are
C when touched, the metallic piece will be felt hotter than the wooden piece
D when the two pieces are removed from the open to a cold room, the wooden piece will lose heat at a faster rate than the metallic piece
Metal is better conductor of heat than wood.
Hence, from metallic piece, more heat is conducted into the body than from a wooden piece.
So, alternative (c) is correct.
Black painted wooden piece will act as a black body. It will absorb more heat as compared to a polished metallic piece when placed in open in bright sun.
Now, according to Kirchhoff's law, as a good absorber is also a good emitter. Hence, wooden piece will lose heat at a faster rate than the metallic piece.
So, alternative (d) is correct.