How many g of NaOH is needed to make 300.0 mL of a 20 % (w/v) solution? I'm so lost right now I have absolutely no clue

You're making this harder than it is. What's the definition?

20% NaOH w/v means 20g NaOH/100 mL solution. You want 300 mL solution so you will need ? grams NaOH. Would you believe 3*20 = 60? or if you want it as an equation it is
20 x (300/100) = 60.
If 20/100 is the def then 60/300 must be right. Don't let chemistry with all of the symbols strike fear into your heart and don't believe you neighbors just because they tell you chemistry is hard. You just think it through and don't get intimidated.