Her equation is wrong. It should be
(20)(0.85)(1.06) = 18.02
20 x 0.85 = 17, the price after the 15% discount. Cat’s equation added 15%.
You could also do 20 x 0.15 = 3, the amount of the discount, and subtract from $20.
17 x 0.06 = 1.02, the amount of tax
Total cost = 17 + 1.02 = 18.02
This tax part is represented by the 1.06 in the equation. The sale price + 0.06 of that price in tax.
Let me know in the comments if you have questions.