As with any task, break it down into smaller bits.
1) Read your file
2) Break it into words.
3) Identify different / duplicated words
4) Count them.
5) Find the highest count.
At each stage, get the ones before written, coded, tested , and perfect before moving on.
Now, the first I'm going to assume you know how to do.
The second (given your sample data) is simple: look at the String.Split Method (System) | Microsoft Docs
The third is more complicated, and there are a whole load of ways to do it.
The fourth is probably most easily done as part of the third, once you have the third working.
The fifth is pretty trivial when the rest is done.
How would I do it? I'd use Linq, and a single line of code for 3, 4, and 5 all together - but that won't get you anywhere with your homework if you aren't good with loops yet!
So: Set up a pair of arrays, one holding strings, one holding integers (or better, a class holding a string and an integer then create an array of them if you've covered that yet).
Loop through your words, and see if each one is in the strings array already. If it aren't, add it.
When that's tested and working, add a counter: set the relevant integer to one when you add the word to the collection, increment it if it's already there.
Finally, look for the highest number in the integers collection, and print the associated word.
It's not complicated, not really - but it's your homework, so I'll give you no code!