Given ~ and ab = 20, ca = 8, and us = 9, what is st?
does anyone know?

ST would be 22.5. 
Assuming ΔABC and ΔSTU are similar, they have to be proportional, so you could create a proportion to figure it out: 8/20=9/? (if you need to know how I got that, message me). Then you could cross multiply. 9x20 is 45, so that means that the measure of ST times 8 has to equal 45. If you divide 45 by 8, you get 22.5, so that makes the measure of ST 22.5.
(Sorry if that was confusing, I can always take a picture of my work if you need further explanation)