Let’s look at (b) first. Suppose that $3$ shops were not considered after the first round; then $3$ shops received at most $1$ vote each, leaving at least $5$ votes that must have gone to the other two shops. No matter how you split $5$ votes between $2$ shops, at least one of the shops must get at least $3$ votes: if each of them got $2$ or fewer, that would be a total of at most $4$.
Now for (a). If a shop gets $5$ or more votes in the first round, it must be the absolute winner: no other shop could get more than $3$ votes. What if a shop gets $4$ votes? It will be the absolute winner unless another shop also gets $4$ votes. Thus, one way to have no absolute winner is to have the $8$ votes evenly split between two shops.
What if the highest number of votes received by any shop is $3$? If that shop is not to be the absolute winner, there must be another shop with $3$ votes, and the other $2$ votes can either go to a third shop or be split between two of the other shops. In other words, the votes must split $3,3,2$ or $3,3,1,1$. I’ll leave the last little bit to you: is it possible to have no absolute winner when the highest number of votes received by any shop is $2$? What about $1$?