Luis and liz each rounded 635,974 to the nearest ten thousand. louis wrote 63 and liz wrote 64.who is correct ? explain the error that was made

Liz is correct. Louis accidently rounded down instead of rounding up. He should've rounded up because 5 or more is rounding up.

Liz is correct.
Louis was wrong because he didn't round correctly. Look at the ten thousandth place which is the current 3 in (635,974). In order to round to that place you must look at the number to its right which is the 5.
If that number to the right of the 3, is 4 and under then you leave the 3 as it is and the number would be 630,000. However if the number to the right of the 3 is 5 or higher, then the 3 is rounded up to a 4 and the number would become 640,000.