In the nitration of compounds such as naphthalene and anthracene, how can you determine which would be the major product? I tried drawing resonance structures for the intermediate formed because stability of intermediate determines which product will be major, but this became too hard for me as there were too many resonance structures and I couldn't really compare them. Can someone please help?
In the electrophilic substitution of polycyclic aromatics, when drawing resonance structures keeping as many benezene rings intact as possible is important. Note too that a naphthalene ring isn't as "good" as two separate benzene rings.
Look at the structures below, electrophilic attack at the 1 position in naphthalene (top row of drawing) allows you to draw 2 resonance structures with a benzene ring remaining intact (4 if we count structures with the double bonds simply shifted in the intact benzene ring); attack at the 2 position (middle row in figure) only has 1 resonance structure (2 if we count structures with the double bonds simply shifted in the intact benzene ring) with a full benzene ring intact. Hence, electrophilic attack at the 1-poisition is preferred in naphthalene.
Applying the same considerations to anthracene, we see that only attack at the central ring position allows 2 full benzene rings to remain intact in the possible resonance structures. Consequently electrophilic attack at anthracene's 9-position is preferred.
When you compare the stability of the carbocation intermediates of polycyclic aromatic compounds, you have to consider if the aromaticity of one of the rings is sacrificed in order to delocalize the positive charge. If this is the case, the intermediate is less stable.
For naphthalene, for example, substitution at C1 is favored, because the cation is stabilized by allylic resonance and the aromatic character of the second ring is maintained. After attack of the electrophile E at C2, the charge in the resulting cation is delocalized without retaining the aromaticity of the second ring (it no longer has 6 π electrons). Hence, this C2-substituted intermediate is less stable (source).
You can make analogous considerations for anthracene, except that there is a third position for substitution, namely C9 in the middle ring. Delocalization of the charge on this position creates a cation with two intact benzene rings, which favors substitution at this position.
To supplement Jannis Andreska's excellent answer, you can consider the total number of resonance structures available to both carbocation intermediates.
Nitration at position 1 produces a carbocation that has 7 total resonance structures, 4 of which appear to preserve the aromaticity of the second ring.
Nitration at position 2 produces a carbocation that has 6 total resonance structures, 2 of which appear to preserve the aromaticity of the second ring.
You can do the same analysis for anthracene, and you will probably find that nitration at position 9 (on the middle ring) is favored.