“Rina, let me call you right back.”
You get a phone call while you're on the line with someone else. You answer it, but you want to finish the other conversation first.
Rina, let me call you right back.
When you see or hear the words "Let me...", you may think that the speaker is asking for permission, but that's not true. This phrase is used in both casual and formal situations to announce what you're going to do:
Let me give you a few examples.
This is more confident-sounding than "I'd like to ___". It's more polite than "I'm going to ___."
You can say a person's name to get their attention in a phone conversation or a face-to-face conversation. For example:
A: ...and then I told her that if they weren't going to pay for me to fly, I wasn't —
B: Selena, hold on a second. Someone else is calling me.
Calling someone "right back" means calling them very soon after they called you.
You can call someone "right back" if you missed their call, or if you spoke to them but had to stop the call before your conversation was completely finished.
You can also say "call (someone) back", which sounds slower than calling them "right back":
Rina, let me call you back later this afternoon.