Thanks for all your great work and comments. I think you are doing an excellent job!
Here are a few of my comments on this essay
Introduction: Thesis Sentence
It is widely believed that women are the principal people in family who take care of all members’ routines and households. Nevertheless, in my opinion, both men and women should have equal distribution to the house’s duties. Some solutions should be soon implemented in order to promote the gender equality at home.
I would remove the passive in the first and third sentences. You have linked smoothly from the first to the second sentence and your opinion is clear - great! However, I don’t like the ‘some solutions’ wording in the thesis sentence. Tell us! Don’t leave us in suspense!
A strong thesis sentence guides the reader to the layout of your essay. You have five paragraphs: it would be good for the reader to know what to expect in each paragraph.
Here’s one possible rewrite:
In many homes, women do the bulk of the work. In my opinion, however, both men and women should have equal responsibility for the house’s duties. To promote the gender equality at home, we need more education, more economic power, and more assertiveness.
I've kept the order from your paragraphs (Para 2: education; Para 3: money; Para 4: communication).
- …to promote the gender equality at home. → to promote gender equality at home.
Word Choice/Word Form/Usage
Cohesion in IELTS means linking between sentences and inside sentences. Have a look at the official IELTS descriptors for Task 2 Writing here, under Cohesion.
It is essential to raise people’s awareness about gender equality through education, because many people consider house duties as women’s tasks. As a result, education helps to raise men’s awareness about their responsibilities at home, so they may be willing to share households with their wives.
Using “as a result” here is not really accurate – we need to change the tense to link it to the previous sentence. We could rewrite it like this:
It is essential to raise people’s awareness about gender equality through education, because many people consider house duties as women’s tasks. Education would help to raise men’s awareness about their responsibilities at home, so they would be more willing to share the responsibilities with their wives.
Ideas and Organization
In Paragraph 4 , you wrote:
Women should have their own skills in order to encourage their husbands to do housework. For example, husbands can join hands to take care of some kinds of households such as dish washing, tiding up, and guiding children to do homework.
The second sentence doesn’t link smoothly from the first. What skills should women have? You described what men could do. Do you mean that women should be able to stand up for themselves or communicate better?
I think you could write a stronger conclusion. The word ‘actions’ is weak - tell us! Specify! You wrote:
We should take actions as soon as possible to make a better life for all women in the world.
Here’s one possible rewrite:
If women earned more and were better able to speak up, then we would find more husbands in the kitchen - and not just at the fridge. OR
If women had more financial power and were more assertive, men would soon learn to share responsibility at home.
Why did you go for a five-paragraph layout? It’s not a criticism - it’s just an enquiry. Why five paragraphs rather than 4 or 6?
Overall, clearly organized and argued. Try to avoid passives: "Passives, like cliches, should be avoided like the plague."