12 is your smallest number so you know that it can be no larger than 12. It also must be included in 12's factors so I would start there.
12's factors include 1,2,3,4,6, and 12. I would start just plugging them in
one always works so but we could always use it as a backup
20/2=10 so that works
26/2=13 so if worst comes to worst we have 2
20/3=6.666 so that doesn't work
20/4=5
26/4=6.5 so that doesn't work either
Because 3 doesn't work and 3 goes into 6 we know 6 doesn't work either
The same thing happens with 12 so 12 doesn't work either.
Now we just go back and find the numbers that worked (1 and 2) Out of those numbers 2 is the largest so it is our greatest common factor.