Telling people your telephone number can be described as "giving out your number".
The phrasal verb "give out" means to give something to a lot of people. For example,
They're giving out free samples in the lobby. You should go get one!
I've gotten a lot of clients just by giving my business card out at parties and events.
The phrase "give out your number" is common in relation to dating. Women are usually careful about "giving out" their phone number to men, because the men might call to ask them out a lot. Men are usually the ones who ask for a woman's telephone number. Men don't usually have to worry about women calling them too much. So the speaker in this example is making a little joke.