Is this how they're teaching math now? I don't think I like it, but that's another convo...
What they're doing is simple: they're adding in increments to bring you to numbers where the math is easy. For this simple problem it's more complicated than the old way, but for a harder example it teaches kids how to approach it.
13,776 - 8,913
8913 + 2 = 8915
8915 + 5 = 8920
8920 + 80 = 9000
9000 + 1000 = 10000
10000 + 3000 = 13000
13000 + 700 = 13700
13700 + 70 = 13770
13770 + 6 = 13776
Add up the numbers after the plus sign: 2+5+80+1000+3000+700+70+6 = 4,863
Thus, 13,776 - 8,913 = 4,863
....
Now, the better at math you become, the more of those steps you can combine, so it's fewer steps, but the point is to teach kids how to reason through large number arithmetic. Kids often see large numbers and throw their hands up, but the decimal system makes even large numbers fairly simple to add/subtract