Question-In how many ways can eight people be seated around the table?
As the question state only table, I do not know whether it is a rectangular table or circular table as the answer can differ from the category of the table.
As for the circular table, the answer is = $7!$
As for the rectangular table with 4 people on each side, the answer is = $4\times{7}!$ = $4\times\underbrace{7\times 6\times 5\times 4\times 3\times 2\times 1}$ = $20160$.
Which one is correct teachers?
Well, according to me: If you generally search the Web or look at such related problems, if they say: Find the number of … seated around a table, it generally refers to the fact that the people are seated around a circular table. See for example, this earlier question.
But, generally teachers and problem books specify when students are to work on problems other than the above by explicitly stating the fact: Find the number … seated around a rectangular table or around a square table with two at the sides and the like. See for example, here.