Add the biggest place values first, keeping a running total — so you speak the answer in the order you'd read it, instead of starting at the units and carrying backwards.

The written algorithm goes right-to-left and makes you hold carries. Doing it left-to-right keeps a single running total:

468 + 357 → hundreds: 400 + 300 = 700 → tens: 60 + 50 = 110, total 810 → units: 8 + 7 = 15, total 825.

You only ever track one number (the running total), and it grows in reading order.

Pitfall: the popular claim that left-to-right "never needs carrying" is only true when each column stays single-digit — here the tens column (110) does roll into the running total. You still combine; you just don't juggle separate carry marks.