Answer
a) $H_2O$
b) $C_6H_{14}$
c) $H_2O$
d) $C_6H_{14}$
e) $H_2O$
f) $C_6H_{14}$
Work Step by Step
a) $Cu(NO_3)_2$ is an ionic compound due to it being composed of a cation ($Cu^{2+}$) and an anion ($NO^-$) making it most soluble in the polar $H_2O$.
b) $CS_2$ is a nonpolar compound due to its linear shape making it most soluble in the nonpolar $C_6H_{14}$.
c) $CH_3OH$ is a polar compound due to its polar alcohol functional group making it most soluble in the polar $H_2O$.
d) $CH_3(CH_2)_{16}CH_2OH$ is a relatively nonpolar compound because although it has a polar alcohol functional group, its long nonpolar carbon chain makes it predominantly nonpolar making it most soluble in the nonpolar $C_6H_{14}$.
e) $HCl$ is an ionic compound due to it being composed of a cation ($H^+$) and an anion ($Cl^-$) making it most soluble in the polar $H_2O$.
f) $C_6H_6$ is a nonpolar compound due to it being composed of only nonpolar $C-H$ bonds making it most soluble in the nonpolar $C_6H_{14}$.