Answer
m$\angle$ACD = 96$^{\circ}$
Work Step by Step
First, let's use the given hint and change our given diagram accordingly. Now we have line c parallel to lines a and d. Let's also create point R above point C on line c, to make labeling angles easier.
Next, we can use some of the properties of parallel lines to help us.
We know $\angle$BAC is congruent to $\angle$RCA because alternate interior angles are congruent. m$\angle$BAC=42$^{\circ}$, and congruent angles have the same measure, so m$\angle$RCA=42$^{\circ}$ as well.
Using the same property, $\angle$EDC is congruent to $\angle$DCR. Therefore, both have a measure of 54$^{\circ}$.
Using the angle addition postulate, m$\angle$RCA + m$\angle$RCD = m$\angle$ACD.
Using substitution, 42$^{\circ}$+54$^{\circ}$ = m$\angle$ACD.
Therefore, m$\angle$ACD = 96$^{\circ}$
