According to modern people, who or what determines the outcome of people's lives? is that similar to or different from what the ancient greeks thought? do you believe in fate? why or why not?

Yes.  We all have fate. Each and everyone of us.  It doesn't matter what I belive it's what you belive!!

Explanation:

faulty parallelism is a construction in which two or more parts of a sentence are equivalent in meaning but not grammatically similar in form.

the correct version of this faulty parallelism in the sentence is:

the hikers knew that the hike was six miles, that it usually required the entire day, and it would not be wise to start after 10: 00 a.m.

the problem is the last sentence, the first two have a basic subject+verb+object structure.

so, to give a proper balance to the structure, or better said, to give a parallel structure, we must write a basic s+v+o structure in all three sentences:

the hikers knew that the hike was six miles, that it usually required the entire day, and it would not be wise to start after 10: 00 a.m.