why are these phrases in the parenthesis wrong?

Delagado's dilemma was (like many other) young writers. Should this one be "like that of many other" instead of what I have in the parenthesis?

Air pollution caused by industrial fumes has been studied for years, but only recently (has) the harmful effects of noise pollution become known. Should this one be "have" instead of "has?"

One challenge that writer Eleanor Wong Telemaque faced was (how preserving) her ethnic identity while becoming more accessible to readers who are accustomed to writers from other cultural backgrounds.

All states impose severe penalties on drivers who do not stop when (he or she is) involved in accidents.

You're right about the first two corrections. In the second example, the subject of the verb in the second clause is effects.

In the third example, you don't need the word how.

In the fourth example, the pronoun in the parentheses should refer to its antecedent -- drivers. What pronoun do you think should be used to refer to drivers?

they are

The phrases in the parentheses are wrong for the following reasons:

1. "Delagado's dilemma was (like many other) young writers."
The correct phrase should be "like that of many other young writers." This phrase clarifies that Delagado's dilemma is similar to the dilemma faced by many other young writers.

2. "Air pollution caused by industrial fumes has been studied for years, but only recently (has) the harmful effects of noise pollution become known."
The correct phrase should be "have" instead of "has." The subject of the verb in the second clause is "harmful effects," which is plural, so the verb should also be plural.

3. "One challenge that writer Eleanor Wong Telemaque faced was (how preserving) her ethnic identity while becoming more accessible to readers who are accustomed to writers from other cultural backgrounds."
The word "how" is not necessary in this sentence. The correct phrase should be "preserving" instead of "how preserving."

4. "All states impose severe penalties on drivers who do not stop when (he or she is) involved in accidents."
The pronoun in the parentheses should refer to its antecedent, which is "drivers." Instead of using "he or she," a more inclusive pronoun like "they" can be used. The correct phrase should be "when they are involved in accidents."

By identifying and understanding the grammar rules behind these corrections, you can enhance your writing skills and avoid common mistakes.