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This is a good question, but PLEASE don't get too wrapped up in all this combinations stuff over a problem like this. The order doesn't matter, because when you grab two books, then who cares what order you hold them in. The question would have to be more specific in order for order to matter.

Since there are only 6 books, I would just chart it out and leave the formulas at home:

a-b
a-c
a-d
a-e
a-f

and

b-c
b-d
b-e
b-f

That's nine. I didn't do b-a here, because we did it already in the first one, so that's the only place where order makes a difference anyway. If the question doesn't include the one instance where you get both, then you can elliminate it anyway, so the answer is 8. I'm not sure which one this is by the wording.

both the methods described above doesn't sound good to me :-8)

The easiest method is just 2*4 (A or B hence 2 and out of the four remaining, 1 book can be picked in 4 ways)

I guess Damit has already got the method, and just needs to know whether the order matters in this case. Well, my answer is NO

When the question is framed as "number of ways in which any two books can be picked" I do not think order matters. However, if these were subjects for an exam, and say A is a prerequisite for D then most definitely the order matters. If no condition is mentioned on the pick, Order does not matter!