1. He can do boxing very well.

2. He is boxing with his friend behind a taxi.
3. He is practing boxing at a boxing center.
4. He likes boxing very much.
5. Why is he learning boxing?
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Are they all grammatical?

6. He can do taekwondo very well.
7. He is learing taekwondo with his friends at the taekwondo center.
8. He is practicing taekwondo on the playground.
9. He is doing taekwondo with other members at the taeknowdo center.
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Are they all grammatical? Would you correct some errors? Thank you.

1 is not quite right, but 2-5 are all grammatically correct.

In place of 1, you should write, "He boxes very well." (Don't put "do" and "boxing" together.)

6-9 are all grammatically correct.

1. He can do boxing very well.

2. He is boxing with his friend behind a taxi.
3. He is practicing boxing at a boxing center.
4. He likes boxing very much.
5. Why is he learning boxing?

All of the sentences in the first set are grammatically correct. However, sentence 2 could be rephrased for clarity: "He is boxing with his friend behind a taxi." In this case, it would be better to use the present progressive tense "is boxing" instead of the simple present tense "does boxing" to indicate an ongoing action.

For the second set:

6. He can do taekwondo very well.
7. He is learning taekwondo with his friends at the taekwondo center.
8. He is practicing taekwondo on the playground.
9. He is doing taekwondo with other members at the taekwondo center.

Again, all of these sentences are grammatically correct. However, in sentence 9, it may be better to use the word "practicing" instead of "doing" for clarity: "He is practicing taekwondo with other members at the taekwondo center."