"She wants to be able to think quietly."
Translation:Ze wil rustig na kunnen denken.
Why wil and not wilt?
"De werkwoorden willen, zullen, mogen en kunnen zijn echter uitzonderingen op de regel"
My attempt at a translation: The verbs willen, zullen mogen and kunnen are exceptions to the rule.
I should have probably already known that but I didn't so I've posted for other people.
Yes, willen, zullen, mogen en kunnen are irregular. If your Dutch is advanced enough, an explanation why can be found here. In short, those verbs haven't always had a present tense; at some point in history, people decided that a present tense would actually be useful so they took the subjunctive and just used that as a 'normal' verb - subjunctives don't conjugate, hence it's "hij/zij/het wil" and not "hij/zij/het wilt."