Rewarded behavior will increase, ignored behavior will decrease.
By that I mean: when your 6 year old throws a tantrum, you are paying attention to her, telling her to stop, giving her a swat, getting aggravated and angry, and generally "rewarding" her with attention and drama. Rewards in this case do not mean toys and prizes. The reward is that now mommy is getting red in the face, interacting with the child, and things are suddenly all about the child. The child is the center of everyone's attention.
Next time it happens, ignore her as if she were nothing more than a picture on the wall. Don't respond, blink, tense your shoulders, speak, or make eye contact. Nothing. Find something to do. Peel potatoes for supper and hum a little happy tune. Knit. Iron. Read People magazine. Dust the furniture. Wash the dishes. Play a game on your phone.
Now, the INSTANT that the child stops to take a breath, or to look and see if you're noticing this ridiculous tantrum, pay attention to her. Don't talk about the tantrum. Say something light-hearted like "so should we have carrots or beans with the chicken tonight?" or "oh, remember we have to go buy Sally's birthday present this weekend" or "I wonder how Grandma's feeling? We should call her later." Get on her eye level, interact with her calmly. The INSTANT the tantrum begins again, remove all eye contact, interaction and talk.
It will take an Oscar-winning performance. Believe me. When she realizes that the tantrums don't get anyone's attention (and your husband or other adults in the home have to be on board too), they'll disappear. But be warned, they may get worse in the initial steps. "Mom, you don't seem to be hearing me scream. Can you hear me NNNNNOOOOOWWWWWWW?" That's to be expected. It doesn't mean the plan is failing, it means it's working.
Reward her non-tantrum moments with your attention, your time and your eye contact. Simply include her in the conversation, talk to her about whatever it is you're doing, talk about the weather, whatever. That's the reward.
Next time you're in the grocery store, observe what our daughter's doctor called the Grocery Cart Theory. Toddler in cart, mom is shopping intensely, toddler starts fussing or screaming, mom stops shopping and pays attention to toddler and offers crackers or sings a song. Toddler is quiet for the moment, mom resumes reading labels and looking at coupons. That's the exact opposite of what should happen. It should be: toddler in cart, mom is shopping but talking with toddler. "Wow, beans are expensive this week. Look at this funny label. Hmmm...$2 for this item but this larger one is $2.50 so which one is the better bargain? What do you think? I agree. Good decision! High five!" (Doesn't matter that the toddler has no idea what $2 is or what gluten-free means). Toddler starts fussing and screaming for cookies, mom removes all eye contact and communication. Toddler takes a breath, mom resumes interacting with toddler. Toddler learns "oh, I get the reward of Mommy's voice and talk and happy smile when I'm sitting quietly" instead of "I get the reward of Mommy's voice and talk and crazy angry face which is actually pretty funny to a 2 year old when I pitch a fit because I want the cereal with the big red bird on the box".