"Habit" is the key word here. Right now, your daughter is in the habit of having a cartoon on TV while she eats, so to get rid of this habit, you'll need to reinforce the replacement behavior you want her to display, which is eating dinner without the TV on.
We suggest that you don't make a big deal out of it. She, however, will make a big deal out of it and will likely continue to throw tantrums for days with the hope of getting her way (you give up and turn the TV on) just one time. Remain calm and stoic through her tantrums. Quietly yet firmly say, "No more TV during dinner." Model this behavior yourself, too; keep the TV off during all family meals. She will be loud and unpleasant at first, but give her short reminders to eat her dinner during her outbursts. You can let her know that you hear her, so she doesn't feel like you're ignoring her, but then continue to eat or visit with your spouse.
There is no need to count bites or anything, which could cause more of a power struggle. If your daughter starts throwing her food, keep it at a distance and again quietly ask her if she is ready to calm down so she can eat. If so, reintroduce the food in front of her again once she is calm.
If you do give in to her and turn on the TV, it will take twenty more times of trying to reinforce the replacement behavior because kids learn at a very young age that "if Dad gave in last week, I can push him this week." The quicker you shut down this behavior the better; you won't want to end up with a sixteen-year-old daughter trying to manipulate you.
If you decide to implement our suggestion, practice the calming technique of "blowing out candles" with her at least three times a day. To do this, both you and she hold up three fingers and slowly blow out one candle at a time. Practice this when she is calm in the morning, during playtime, or in the car. This technique shows her how to control her emotions, and she'll be less likely to feel like you are trying to control her.
Having the TV off from now on is just a fact. Hopefully, over the next week, you'll notice that her outbursts are less severe and not as frequent.
