We use the -ing for after:
- Some verbs (admit, avoid, fancy, miss, top, practise, enjoy, imagine, keep, hate.
- Verb + prepositions / phrasal verbs (succeed at, apologise for, dream about, think about, look forward to, give up, feel like.
- Adjective + prepositon (good at, interested in, proud of, sorry for, tired of, famous for.
- Some expressions (after, by, instead of, when, I don’t mind, I can’t stand, without, it’s worth, before.
We use the infinitive with to after: (agree, allow, decide, expect, hope, learn, manage, offer, promise, refuse, seem, want, would like, need)
We use the infinitive without to after:
- Modal verbs (must, might, will, should, can, could)
- Other verbs with an object (let, make)