A 12th-level human two-handed fighter has 13 feats.
How many feats does a 10th-level two-handed fighter/2nd-level aegis have if they were human until 10th level and then changed to the elan race?
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A human gets a single bonus feat, at 1st level. You seem to have left this out of your description of a 12th-level human fighter, since a 12th-level human fighter has 14 feats, not 13.
A 12th-level fighter has 13 feats from those levels (the human bonus feat would be in addition to this). There are six feats for their odd levels (1st, 3rd, 5th, 7th, 9th, and 11th), and seven bonus feats from fighter levels (1st, 2nd, 4th, 6th, 8th, 10th, and 12th).
The two-handed fighter archetype does not change the number of feats that a fighter gets; that archetype only changes the bravery, weapon training, and armor training features, not any of the fighter bonus feats.
A 10th-level fighter/2nd-level aegis has 12 feats: the same six feats at odd levels (1st, 3rd, 5th, 7th, 9th, and 11th) that everyone gets, as well as six bonus feats from their fighter levels (at 1st, 2nd, 4th, 6th, 8th, and 10th). The fighter/aegis does not get the bonus feat that the single-classed fighter got at 12th, because they haven’t taken the 12th level of the fighter class. They do not get any bonus feats from their aegis class levels: the aegis class only ever gives one bonus feat, at 5th level, and that feat is always Master Craftsman. The fighter/aegis could get that bonus feat if they continue taking aegis levels and reach fighter 10th/aegis 5th.
Importantly, I have no idea whether or not your human-turned-into-an-elan should still have their human bonus feat. Probably not, but since there is no official rule for such a transformation, and your GM has made this up, you’ll have to double-check with them to see what the ruling is there.
So the human-turned-elan fighter/aegis might have 12 feats or 13 feats, depending.