“We were able to raise just under fifteen thousand dollars.”

You were in charge of planning an event to raise money for a charity. Now the event is over, and you're talking to a friend about how it went. You're telling him about the amount of money you made.

We were able to raise just under fifteen thousand dollars.

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be able to (do something)

"Be able to" means "can". But you can't use "can" with "might". So instead you say "might be able to".

You also use "be able to" when talking about things that you successfully did in the past:

I was able to contact Jesse, and he said he would send them to us right away.

Were you able to find out how much it costs?

And you use "be able to" with other modals like "should", "will", "may", etc."

He should be able to help you.

I won't be able to finish it until some time next week.

raise (an amount of money)

To "raise money" means to get money from investors or donors. Investors are people who lend you money to get a piece of your business, so that they can earn more money later. Donors are people who give their money for a charity, a school, etc.

You can use the phrase "raise money":

We're raising money for cancer research.

Or you can state the amount of money:

We're hoping to raise $100,000 for cancer research.

just under (an amount of money)

"Just under $15,000" might mean $14,600 or $14,900. It's a number that's under $15,000, but very close to it. One reason for using this phrase is to make the number sound bigger than it actually is. "Just under a million" sounds larger than "nine hundred, seventy five thousand" (975,000).