Paradosso is right and the approach is simple.
One more approach which is not simple but holds many concepts is as follows...
A B C D E F be the six ppl and
A and B have to sit together.
Total # of ways n ppl can sit around a table is (n-1)!
therefore ppl can arrange themselves in (6-1)! equal to 5!
this becomes sample set.
join two ppl so that they are one. That is they sit side by side.
Number of ways they can be arranged is 2. AB or BA ---1
Now these two ppl can be treated as one person. so this reduces # of ppl to 5.
AB C D E F
They can be arranged in (n-1)! ways that is (5-1)! ways. --2
Combining 1 and 2
2*4! is total number of favourable events
final answer 2*4!/5!
Wish you all good luck