Answer
(a) To draw the structure of $\textrm{C}_2\textrm{H}_4$ first start by drawing the $2$ carbon atoms ($\textrm{C}$). Equally distribute the $4$ hydrogen ($\textrm{H}$) atoms by placing $2$ on to every $1$ carbon atom.
However, due to the valence electron configuration of carbon, each carbon atom wants to form $4$ bonds total to completely fill its valence shell. Since each of the $2$ carbon atoms only have formed $3$ bonds so far, drawing in a double bond between the carbon molecules ($\textrm{C}=\textrm{C}$) will create the fourth bond both of the carbon atoms need to be stable.
See attached picture.
Work Step by Step
(b) Similar to before, start the $\textrm{C}_2\textrm{H}_2\textrm{Cl}_2$ molecule by placing centrally the $2$ carbon atoms. The attachment of the remaining hydrogen and chlorine atoms could go one of two ways—either both the chlorine atoms are placed on the same side of the molecule, and the hydrogen atoms together on the opposing side, or the chlorine atoms be placed diagonally apart from one another on different sides.
Since we're looking for a trans isomer, remember that "trans" means different. The proper trans configuration will be with the chlorine atoms being diagonally opposite one another, on different sides of the carbon atoms. The hydrogen atoms will be placed to mirror the configuration of the chlorine atoms.
A double bond is again drawn between the carbon atoms as in part (a) to allow the carbon atoms to create a full $4$ bonds and completely fill their valence shells.
See attached picture.
