The question gives us that the total time taken by the person cycling and walking is 5 hours 45 minutes. It also tells us that if the person had cycled both ways, he would have taken 2 hours less.

If we add this two hours to the total time originally taken, we get the time the person would have spent walking both ways, as this time includes the excess time taken by walking compared to cycling. So, the time taken by him to walk both ways is 5 hours 45 minutes plus 2 hours, which equals 7 hours 45 minutes.

Option 1 miscalculates by subtracting two hours instead of adding. Option 3 and option 4 both overestimate the time needed. Thus, the correct answer is indeed option 2: 7 hours 45 minutes.