Gerunds question.. when to use & when not to

Let me shorten these so we can concentrate on the essentials:

1) Owners require another approach to managing assets.

2) Owners require another approach to manage assets.

1) says that owners require something. The something they require is another approach to something -- another approach to the managing of assets, i.e., another approach to the management of assets.

What do they require? -- another approach to asset management
Why do they require it? -- We don't know; the sentence doesn't say.

2) says that owners require something for some purpose. The something they require is another approach. The purpose is in order to manage assets.

What do they require? - another approach. An approach to what? -- We don't know; the sentence doesn't say.
Why do they require it? - so that they can manage assets -- in order to manage assets.

In short, use the one that says what you want to say!

The word "to" is part of the infinitive, so "approach to manage" is a noun ("approach") followed by an infinitive ("to manage"). There is no preposition here. The "to" is not a preposition.

You always use the gerund after a preposition. "Thank you for helping." -- never "Thank you for to help." You use the gerund even after the preposition "to", as in "an approach to managing" -- a noun ("approach") followed by a preposition ("to") and gerund ("managing").

This construction amounts to using a gerund ("-ing" word) as the object of the preposition "to". You don't have any aversion to using gerunds, do you? Eventually you'll get used to seeing this construction, especially if you get around to paying close attention to studying each sentence carefully. Of course, I'm making references to reading this paragraph very carefully.

Did you get the joke?