B. has good ideas! Be sure she is looking into your eyes when you ask her to do something, and have her repeat it back to you, then have her DO it immediately following that exchange. Don't let time elapse, not even five minutes. At four, kids still can have trouble being asked to do something in the future -- even if the future is only 10 minutes away.
As for charts: Be sure that she does not see the chart as punishment. Make it fun and let her help design it; she should participate and pick out the stars or other favorite stickers she wants to use, so it's not like it's imposed on her because she's "naughty." Keep it upbeat and focus instead not on "you will lose a star if you don't do X" but on "you will get a star if you DO X and that puts you one star closer to Reward Z."
Because you must use rewards if you have a chart. No kid will focus if a chart is for its own sake. Make rewards small, but .desirable and most of all achievable. And start very small!
For instance: Do not make her wait a whole week for her first reward. She's new to this and every day is eternal to her. So: If you put away your toys today and tomorrow and the next day, you get a star each time. That is three stars. When you have three stars, you get Reward X." Make X a very small reward, yes, but a reward. "You just got your second star! That's great! Just one more!" Keep up the three-stars thing for a while until she gets the hang of it. Then you can work up to: If you get six stars instead of three, you can have Reward Y." Bigger reward such as a desired outing. She may balk at first and prefer the smaller but more frequent rewards--go with that if it's what motivates her and don't push "But you should wait and get more stars!". Whatever you do, don't .make her wait and wait to amass too many stars or she will lose interest; she can't yet really connect her behavior today to a reward in two weeks' time. She may say she can - but that won't add up to her doing what she needs to do today and tomorrow.
(And as an aside, is she expected to brush teeth on her own? At four some kids do but need supervision. I wouldn't have tooth-brushing be a thing that is subject to a chart and rewards but something that has to happen as you stand there with her, morning and night, and brush your own teeth alongside her and then check her teeth.)
I would have her GET stars for doing things -- but would not take away stars for NOT doing things. Do you see the difference? "Oh, you didn't put the toys into the toy box before bedtime. OK, so that's no star for today but I am sure you can get a star tomorrow!" as opposed to: "You didn't put the toys away so I have to take away the star you got yesterday. Sorry." The latter approach will make her feel defeated and takes away from the success she had in earning the previous star. She'll start to feel that she can never get enough stars --so why try?
She may argue and complain and insist on getting out of bed to do the chore, or put the toys away when she wakes up at dawn and beg for yesterday's star; how you handle that is up to you. But I would not remove stars for a child this age; I'd only give them when earned. An older kid could lose them and understand it, but I would not start out on a reward chart system for a four-year-old by taking away, only by adding (or not, if the thing is not done).
Please don't have more than a very, very few items on the chart. Don't make every little task subject to the chart. Choose your battles with care. Maybe no more than two tasks to start! And be very specific. Don't say "clean up your room" because that totally overwhelms kids, even much older ones than yours. Pick the one chore you want her to do: "Put stuffed animal toys in the red toy box before bedtime." See the specificity of that? She knows exactly what to put where and when to do it. "Put the toys away" could mean two toys or all the toys, under the bed or thrown in the corner. Be very specific.
It is extremely typical for kids her age not to listen and not to heed things. Don't overemphasize it. Be sure to get her full attention and have her do any desired action immediately and with you there -- she is only four. Yes, she's old enough to start learning, but be sure your expectations are very limited, age-appropriate, specific, and supported by positive reinforcement for doing a thing more than punishment for not doing it. And if the chart does not work with her after a long, consistent try, it is not an admission of defeat if you give it up. I found charts worked best between about the ages of four and six, but if she's not ready for it, wait and use one later.