to+infinitive and verb+ing

[Huda2]

hi,
why has been chosen verb+ing instead of to+inf.?
6. I have trouble _____.
to remember my password
to remembering my password
remember my password
x remembering my password

[Cerberus™]

That is idiom: some verbs/predicates happen to take the -ing form, others the infinitive; there is no clear rule. In this case, perhaps you could say that "with" has been left out; a preposition would require the -ing form.

[Milanya]

Gerunds and infinitives can both be used as subjects, subject complements, and direct objects of verbs. The choice of whether to use a gerund or infinitive as a subject, subject complement, or object of some verbs is left to the speaker/writer. This choice can indicate shades of meaning.
But the choice between which to use as a direct object is sometimes dictated by the verb, leaving no choice. Which verbs can be followed by gerunds, which by infinitives, (and which by either) must be memorized. In addition, some verbs require that an infinitive object have a different subject (agent) from that of the first verb, for others no other agent is possible, and for some both are possible. Again, these must be memorized. The general meanings associated with gerunds and infinitives can offer clues, but do not always predict which forms are possible.

Here you can find a detailed explanation, including the list of verbs.
http://www.iei.uiuc.edu/structure/structure1/gerinfvbs.html
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