Current I’ve been assigned 5 pages web design, but my coworker only been assigned two simple html and css task. We got same two weeks to finish it. She joined three months before me. After the task done, my manager ask her to do demo to team, she never mentioned me, and today’s stand up, big team manager said thanks for her demo and work, she didn’t mentioned me too… And now everyone contact her instead of me, and then she told me what others said later.
I feel she’ve been take credit from me..
should I talk with the manager about this? Or I should just quit the job?

It seems you dont have a particular issue with the job but your coworker.

Mention to her and your supervisor that you will own both your mistakes and successes and that you will have an issue if this is not part of their definition of teamwork.
Its a super ignorant thing to exclude your coworkers from a common success. I would instantly recognize it as an ego tour of her but most people dont. And you know what will happen when a mistake occurs, it will be your fault.
You have to do something about these kind of people especially since they are new to the job as well. It really doesnt matter that she did less work than you but that you were excluded from the success. You have to show that they cant do this with you without you mentioning it to her as well as the supervisor. Otherwise you know that she will get the promotion that you deserve in the future and you dont want that.
It will be a great exercise to stand up for yourself as well.

I would do it the following:

- Tell her that she probably forgot to mention you taking an important role in the project as well and that you would like her to mention it as well
- Give her 2 days or 1 good opportunity to mention it. If she doesnt make a brief appointment with your supervisor.
- Tell your supervisor in a very pragmatic manner that you want to be recognized for your work and that you will own both mistakes and successes
- If both show to be ignorant assholes try to not work with them anymore if it is possible. Think about switching teams or even jobs if this isnt an opportunity. You will get angry/depressed if people dont recognize your work and claim your success for their own or if you have a supervisor that ignores your responsibility.

Better make it quick than suffer for too long. Good luck.

Dont badmouth your coworker or blame people, its a delicate walk but you will make it through I promise and you got nothing to loose if you think quitting is an option already.