Using technology as new as space-age fabrics and as ordinary as common dry-cleaning chemicals, scientists and historians, in their attempt at cleaning and preserving the American flag that flew over fort mchenry in Baltimore in 1814, are hoping that it will then last another 200 years.

A.and as ordinary as common dry-cleaning chemicals, scientists and historians, in their attempt at cleaning and preserving the American flag that flew over fort mchenry in Baltimore in 1814, are hoping

B.and as ordinary as common dry-cleaning chemicals, scientists and historians are attempting to clean and preserve the American flag that flew over fort mchenry in Baltimore in 1814,hoping

The Answer is B. But B changed the meaning of the original sentence. “Hoping” was changed to be the verb of the sentence instead of an adv.

In what kind of condition, the original meaning of the sentence should be changed?

If I change A to be “attempting to clean and preserve…”, is A right?

I think you've stated it backwards. It seems as though A give us "hope" as a verb, while B gives us "hoping" as an adverb. Regardless, your question is a good one.

Keep in mind the priority for SC:

Grammar
Meaning
Concision

If a choice violates proper grammar, it is WRONG.

Moreover, we can change the meaning of the sentence when the given meaning is clearly at odds with the INTENDED meaning. Remember, your job is not to preserve the meaning of Answer Choice A, but rather to clarify, if necessary, the INTENDED meaning. The meaning is not clearly expressed in A. Are the scientists really hoping "in their attempt"? Not exactly. Their attempt shows that they are hoping, certainly. In addition, "at cleaning" is the wrong idiom; we want "to clean" here.

Takeaways:
1) slight changes in meaning are okay when we need to satisfy proper grammar.
2) don't get overly stuck on the meaning of A; it's the INTENDED meaning of A that we're after. If A is unclear as to the meaning, we need to correct.

I can not work out the meaning of this sentence? could you explain? Thank you.

i wrote an extensive treatment of this precise topic here.