Several students have asked me when to use infinitive with to, without to or gerund after another verb. The problem is that in most cases there is no explanation. It's just because.
Of course, we know we mustn't use to after auxiliary verbs (with the exception of ought to), but that's about it.
Besides, there are verbs that can be followed by both infinitive and gerund, and in some cases the meaning changes. Look at the examples below:
- I remembered to do my homework and the teacher was very pleased. (I didn't forget)
- I remember playing with my sister when we were little. (a memory)
And one more thing: remember that to let and to make are followed by infinitive without to:
- My parents don't let me go out after ten. I'm so fed up!
- She made me tell her what I knew about George and when I did she started crying.
The link below will take you to some exercises, but there are more on the same page:
https://www.perfect-english-grammar.com/gerunds-and-infinitives-exercise-1.html
I hope this helps.