1.Regarding the conversation we had the other day I have given some thought to your proposal and I have decided we should go ahead with it. 2.Regarding the issue with the broken air-conditioner I have decided to buy a replacement instead of repairing the broken unit. I feel the word "Regarding" is very similar to "about" but it differs in the fact it is normally talking about something that has already been spoken about previously or even just something both people in the conversation know about. For example if I say "Regarding my progress learning Chinese" to somebody who does not know I am learning Chinese it wouldn't really make sense. They would still understand what I am talking about but because it a previously unknown subject to that person I think "Regarding" is the wrong word to use.

"Regarding" is similar to the word "about". It's often used to introduce the subject you're talking about. Regarding language websites, I find italki very useful for meeting other language learners. The teacher talked to the students regarding their homework.