Hello!
In this example "carve out" means 'make time'. The anchor is saying that she is happy you carved out 10 minutes from your schedule, a figurative expression which means that you made a ten minute hole in your schedule to watch the show.
Here is another example: "I am very busy, but I always carve out 30 minutes a day to call my mom; sometimes it is very difficult to find the time and I have to multitask all day at work to make it possible."
I hope that helped, if not, let me know and I will explain in a different way!