can adenine pair with guanine?

No, it pairs with thymine and uracil (RNA).

But if you see the chemical structures of both adenine and guanine, there is a possibility that both of them can form two hydrogen bonds. Moreover the case is same for cytosine and thyamine.

it just doesn't happen

Ok. Thanks for the info.

NP

No, it pairs with thymine and uracil (RNA).

No, it can't.

Everyone has correctly answered your question: NO, A-G will not "pair".
The basic base pairing rules (DNA) are A-T ; C-G
or for RNA respectively: A-U ; C-G

Now what might help with the *WHY* or understanding of the madness behind the science is easily depicted through pictures. Look at how when the opposite strands line up anti-parallel to one another, they chemical structures almost form a puzzle where like pieces fit into their appropriate spots. The chemical hydrogen bonds formed between the strands are similar to the puzzle piece analogy. Look at the pictures and see how the A and T form three hydrogen bonds and the C and G for two, they line up nicely and it is visually apparent why they just "fit".

*note the similarity in the structure of T and U in the second picture and how the A-U base pairing is the same for DNA-RNA.