I'm sure this has been asked before, but the search function is not great. I can't think of another election that might have been flipped due to the 26th Amendment, which lowered the voting age to 18 from the previous 21.
1976 and 2000 are debatable, but almost impossible to say. 1992 is highly unlikely since Clinton won by such a significant margin, though it was the first time that Democrats dominated the under 30 vote.
The question is basically two parts:1. What percentage of the under 21 vote did Obama (or Carter or Bush) win in each state?Likely a large percentage in the case of Obama.
2. What percentage of the electorate was under 21 in the key states?For 2012, these are namely Ohio, Florida, Virginia, and Colorado. I doubt Romney won the under 21 vote in any state he narrowly won (or any state except Utah).
For 1976 and 2000, the analysis is likely too complicated to be worth the effort. There were many close states won by each candidate in each election. We would need to be sure that no states which went to the loser would flip to the winner.
If we can determine that the youth vote did win Obama these states, I'd be interested to see just how many states Romney would win among 21+.
This paper (link to PDF, search for "Romney") says 2012, though results are inconclusive and the paper does not discuss in detail:
https://academiccommons.columbia.edu/download/fedora_content/download/ac:161447/content/Wright_columbia_0054D_11340.pdfMy own research into the question of whether Gov. George Romney supported the amendment is inconclusive. But as the anti-war candidate in 1968, I can imagine he would have been sympathetic to the issue.