Calculates the number of hours and days left, where the total number of hours is 486
ReuseableClass

Each class is (ok, might be) reusable so naming it like this does not have much value. It calculates something... name it simply IntershipCalculator.

And... it's not really reusable either because you write to the console there. You should write to the console somewhere else and let the methods just calculate the results.

NumberOne

This looks to me like a class but it's a method. You should name it appropriatly ie ReadNumberOne.


        //gets input from user
        int accumHours = AccumulatedHours(dayHours, input);
        int remainingHours = RemainingHours(totalHours, accumHours);
        RemainingDays(remainingHours, dayHours);



The comment is misleading. You are not getting here anything from the user but writing results.




Console.WriteLine("1. Enter No. of Days \n2. Use current day");



Why not like so?

Console.WriteLine("1. Enter No. of Days");
Console.WriteLine("2. Use current day");