Preposition + infinitive

Hola Ama

It's correct to use a preposition followed by an infinitive, yes. In fact, you must use an infinitive after any preposition (not a gerund). In this case, though, meaning "by doing something" we don't use any preposition with the gerund as we say in the lesson, and using: por + infinitive here wouldn't work if what you want to say is "by doing something [you achieve something]".

However, if the meaning was slightly different, expressing a "cause", i.e. "He lost weight because he drank two litres of water a day.", you can say:

Here is a lesson on this use of por.

I hope it clarified it.

Saludos

Inma