Translation:That TV is new.
Well, この is used for something that is next to you, その is used when it is next to the other person. So in both cases we would use "this". We use あの for something that is far from the people in the conversation so it's "that". I don't know if it sounds natural in english, but in portuguese it sounds perfectly natural.
I'm not sure if that would be entirely natural English. I think you may have been taught that to emphasise the difference between "ano" and "sono", but in real life you wouldn't be likely to say "that [...] over there" every single time you pointed out something far from you and the person you were talking to, you'd just say "that [...]".