Learn Russian: Я чуть не забыл спросить вас насчёт расценок. - I almost forgot to ask you about the rates.

It follows the preposition насчёт ("about" or "regarding"), which always requires the genitive case. The nominative singular is расценка (rate or pricing), making расценок the genitive plural. Notice the fleeting vowel о inserted at the end of the plural form to make it easier to pronounce.

Could I use о or об instead of насчёт to say "about the rates"?

Yes, you could say о расценках using the prepositional case. However, насчёт is highly natural in spoken and business Russian when zeroing in on a specific matter, translating closely to "regarding" or "concerning."

Why use чуть не забыл instead of почти забыл for "almost forgot"?

While почти means "almost" in terms of quantity or completion, чуть не is specifically used before perfective verbs to show that an action narrowly missed happening. Чуть не забыл conveys that you were on the very edge of forgetting, but caught yourself just in time.

Why does the sentence use the accusative вас rather than the dative вам after спросить?

The verb спросить (to ask a question) takes a direct object in the accusative case for the person being asked. It is a common pitfall to mix this up with verbs of speaking or giving, such as сказать (to say or tell), which take the dative case for the recipient.