“Sorry, I can't hear you. Why don't you text me instead?”

You're talking to your friend on the phone and trying to make plans to meet her. The phone signal is breaking up. You can't hear what your friend is trying to say, so you want her to send you a text message instead. You say:

Sorry, I can't hear you. Why don't you text me instead?

Why don't you (do something)

This is a friendly way to suggest what someone should do. It means "you should ___" For example, if you and a friend are waiting at a concert to meet someone but can't find him, you can suggest:

Why don't you wait here and I'll walk around and look for him?

It might be confusing, because "why don't you" may sound like you're criticizing the listener. But this isn't how it sounds to English speakers. This phrase sounds friendly, light, and casual.

text (someone)

To "text someone" means to send them a text message on a mobile phone. A "text message" is like email but shorter and can be sent to the person's phone number instead of to an email address.

This is a phrase that has only started to be used this way in the last 5 years or so. Before that, the word "text" was only a noun. But now, "text me" is a common phrase for people who use mobile phones.

(do something) instead

To "(do something) instead" means "don't do that, do this". In the example above, when you suggest "text me instead" it means that you want your friend to stop talking on the noisy phone connection, and start texting you.