There is more than one correct answer to this question, which is even hinted at in the question when it says to fill the blank "with a coordinating word or phrase." The simplest way to do this is by using the conjunction "so".
Some people exercise too hard, so they may become ill or injured.
Because there are two independent clauses connected by a coordinating conjunction ("so") you need to put a comma before it.
You can also choose to use a word like "consequently" in the place of "so". I prefer this option myself. However, if you choose to do this, you must punctuate it like this:
Some people exercise too hard; consequently, they may become ill or injured.
Because "consequently" is an adverb, you need to include a semicolon to keep it one sentence.
If you want to answer it with a coordinating phrase, you could write something like this:
Some people exercise too hard; because of this, they may become ill or injured.
When using coordinating words or phrases you always have many options. A lot of these words have similar meanings, and you have to deduce which is the best fit by the nuance of the sentence and your trained ear.