The question and the solution are attached in this post.
I don't understand the solution to question a) ii., could someone please explain it to me?
It's just cumbersome notation: note that since ABCD is a paralellogram, it must be that $\displaystyle AD=BC\,,\, \|AD\|=\|BC\|\,,\,AD//BC\Longrightarrow \overrightarrow{AD}=\overrightarrow {BC}$ , and
putting $\displaystyle D=xi+yj$ , we get that $\displaystyle \overrightarrow{AD}=(x-4)i+(y-2)j=-6i-2j=\overrightarrow{BD}\Longrightarrow x=-2\,,\,y=0\Longrightarrow D=-2i$
Tonio