My question is quite simple but I want to have my answer clarified to
make sure it's right. If A={1,2}and B={f,g,h}, what is the Cartesian
product of A X B? My answer is A X B = {(1,f),(1,g), (1,h), (2,f),
(2,g), (2,h)}. I'm not sure of the notation being correct.Is this
answer correct?

Yes, it is correct.
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In mathematics, the Cartesian product (or direct product) X × Y of two
sets X and Y is the set of all possible ordered pairs whose first
component is a member of X and whose second component is a member of
Y.
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look in:
http://en.wikipedia.org/wiki/Cartesian_product

Just so.

I'll make the link provided by clovek-ga "live":

[Cartesian product -- Wikipedia]
http://en.wikipedia.org/wiki/Cartesian_product

Note that the cardinality of (number of elements in) the Cartesian
product is the product of the cardinalities of the two sets.  More
generally we can speak of the Cartesian product of more than two sets,
replacing the order pairs (x,y) of one element from each respective
set with an order n-tuple (eg. triple, quadruple, etc.), which extends
in the infinite case to a "sequence" indexed by the family of sets
being "producted".

regards, mathtalk-ga