An elevator starts at the 6th floor. it goes up 7 floors twice, and then it goes
down 10 floors. a second elevator starts on the 20th floor. it goes down
5 floors 3 times, and then it goes up 12 floors. which elevator ends on a
higher floor? explain how you know.

Well let's see what floor each one lands on and figure out which one is higher.

Something to note:

down = subtracting

up = adding

if something says it's doing something more than once, add it the number of times it's doing that thing. (You can also multiply it by that number but the adding way is a bit easier to understand and explain)

Elevator 1:

6 + 7 + 7 - 10 = 10

Elevator 2:

20 - 5 - 5 - 5 + 12 = 17

Elevator 2 ends on a higher floor (reasoning above)