carry out = to do something that is part of a plan; follow an order

These business managers are carrying out a plan for the expansion of their company.

catch on = start to understand.

At first, Abbas and Dominique had trouble understanding how to learn English with this website, but then they quickly caught on.

come on = hurry; stop doing something. Sometimes used when asking or pleading for something.

"Come on! Please eat your food!"

 come to terms (with) = to learn to accept. Used with difficult situations.

When there’s a war, many people have to come to terms with the sudden death of a family member.

come up = to happen quickly, suddenly, or soon.

Linda has an important meeting coming up next week and she has to prepare for it.

 come up with = to have an idea or to create an idea

She’s trying to come up with some new ideas for teaching English.

cut down on = reduce; do less of something

If he doesn’t cut down on his smoking or quit completely, he’s going to suffer from illness later in life.

cut off = to stop someone; to be rude and get in front of someone; to interrupt.

He got really mad at the driver who cut him off at the intersection.

I was talking on my cell phone when suddenly I got cut off.