Which of the following molecule has the maximum dipole moment?

The dipole moment depends on the charge and distance between the central atom and side atoms. But the charge is more prominent than distance. It is determined as polar and non-polar molecules. It can be determined by the geometry of the molecule.

In case of ${\mathrm{NCl}}_3 \& {\mathrm{NH}}_3$ the electronegativity difference between $\mathrm{N}-\mathrm{H}$ is higher than the electronegativity difference between $\mathrm{N}-\mathrm{Cl}$ bond so the shared pair of electrons shifted towards chlorine in case of  ${\mathrm{NCl}}_3$ and in case of ${\mathrm{NH}}_3$ it will be towards Nitrogen. So, for ${\mathrm{NH}}_3$ the net dipole moment will be towards the direction of lone pair and will be added up into the dipole moment of lone pair while in case of ${\mathrm{NCl}}_3$ the moment due to three bond pairs will be in opposite direction to the dipole moment of the lone pair, and it will be subtracted results in lower value of net dipole moment.

In case of ${\mathrm{CS}}_2$, it has the linear shape and so their moment is balanced and so net dipole moment is zero.

In case of ethane $\left({\mathrm{C}}_2{\mathrm{H}}_6\right)$, the electronegativity difference between carbon and hydrogen is minimal so unbranched alkanes have zero dipole moment. 

Hence, ${\mathrm{NH}}_3$ has maximum dipole moment among the given options.