Compatible numbers are number that are easy to add together.
If I change 87 to 90 and 34 to 30 I have compatible numbers
90 + 30 = 120. I would probably just change the 87 to 90 since I could to 90 + 34 mentally and get 124 which is closer to the exact answer.
222 + 203 - becomes 220 +200 = 420
May I suggest that you can also balance the numbers: when you change 87 to 90 you added 3. To compensate, subtract 3 from 34 and get 31. 90+31= 121, the exact answer.
222 becomes 200 so you lowered it by two. To compensate add 2 to 203. Now you have 220+205= 425 which again, is the exact answer. Use estimation is needed but what I just showed you works well to and give you the exact answer.
One more: 199 + 306 = 200 + 305 = 505 (exactly) Instead of 200 + 300 = 500 which is a close estimate using compatible numbers.