She put on her hat and left without saying a word.
Prepositions are followed by nouns. A gerund is the noun form of a verb — so after any preposition, use -ing.
He managed by asking for help.
She is very good at making sculptures.
good at it
→ good at making
If it fits after the word, that word is a preposition.
by, without, before, after, in spite of, instead of, except for, apart from
apologize for, talk about, insist on, succeed in, give up, end up, keep on, put off
I want to go.
want, hope, decide, need, promise
I look forward to going.
look forward to, be used to, object to, in addition to
He used to work nights = past habit. He is used to working nights = he's accustomed to it.
I look forward to hear from you.
Correct: I look forward to hearing from you.
She is very good at to cook.
Correct: She is very good at cooking.
He left without say goodbye.
Correct: He left without saying goodbye.
He's responsible ^ checking the invoices.
Correct: He's responsible for checking the invoices.
Say the answer out loud — then tap to check.
He apologized forA arrivingB late and insisted on payC for everybody's taxi himselfD.
Cand insisted on pay → and insisted on paying
✓ preposition + -ing
Everyone in the offices were opposedA to closing the canteen, butB the decision hadC already beenD made.
AEveryone in the offices were opposed → Everyone in the offices was opposed
✓ everyone is singular → was
After checkingA the figures twiceB, the accountant was confidentC about to signD the report.
Dabout to sign → about signing
✓ about is a preposition → -ing
Use a preposition + gerund in every answer.
Find the preposition first — then add "-ing".