correct answer is: c) 750 machine parts

Explanation

Here,
Days and Machines Parts are Directly Proportional.
Hours and Machines Parts are Directly Proportional.
So that,
4\;:\;7\;\&\;7\;:\;6\;:\;:\;500\;:\;x
\rightarrow\large\frac{4\times7}{7\times6}=\frac{500}{x}
\rightarrow\large\frac{2}{3}=\frac{500}{x}
\rightarrow 2x=500\times3
\rightarrow x=\large\frac{500\times3}{2}
\rightarrow x=750 Machines
\therefore If the man works for 7 days at the rate of 6 hours per day, then 750 machine parts will be produced.
Ans: 750 machine parts will be produced.

Other forms of this specific math question are:

1. If a man typically produces 500 machine parts in 4 days working 7 hours per day, how many machine parts will be produced if he works for 7 days at the rate of 6 hours per day?
2. How many machine parts will be produced if a man, who can make 500 machine parts in 4 days working 7 hours per day, works for 7 days at the rate of 6 hours per day?
3. Suppose a man can make 500 machine parts in 4 days working 7 hours per day. How many machine parts will be produced if he works for 7 days at the rate of 6 hours per day?