Great question! The trick really only works as long asThe units digits of the two numbers sum to 10, and The rest of the numbers, apart from their units digits, are the same.
... like you could try writing 62 and 64 as 60+2 and 60+4, but when you multiply them the terms won't add and cancel nicely like they did in Prof. Loh's explanation.
I hope that made sense to you; if it didn't I'd be happy to clarify.
This trick is slightly related to Difference of Squares, but also very different. It does not actually currently have a name... so I guess you could call it Prof. Loh's Trick.