This is a jukugo word that uses the on'yomi readings of the kanji. You haven't learned this reading for 底 yet, so here's a mnemonic to help you:
Thoroughness is important when you're making tater (てい) tots. Each tater has to be cut carefully into little pieces then smashed back together again. Don't even get me started on the completeness I feel when I finish and eat them. Mm.
She can’t go out until she thoroughly applies her make-up.