Question

Any woman who understands the problems of running a house will be nearer "to understand" /"to understanding" the problems of running a country. Infinite or gerund? And why?

Answer 1

gerund.

A gerund functions as a noun. As such, it can function as both a subject or as an object of the sentence.

In your sentence, 'undertanding' is the object of the sentence. (specifically, the object of the preposition.)

Any woman who understands the problems of running a house will be nearer to understanding the problems of running a country.

Explanation:

For clarity and simplicity, consider this comparison ....

S V prep. O

Any woman ......... will be nearer to understanding ....

S V prep O

I walked to (the) store.

-------------------------------------------------------------------------------------------------------- BTW ... the word is 'infinitive,' not 'infinite.'