How many grams of copper can be dissolved by 20.0 mL of a 69.6% (by mass) nitric acid solution that has a density of 1.41 g/mL?

What's the molarity of the HNO3? That's

1.41 g/mL x 1000 mL x 0.696 x (1/molar mass HNO3) = about 16 M but you should calculate it more accurately.

What's the equation?
Cu + 4HNO3 ==> Cu(NO3)2 + 2NO2 + 2H2O

mols Cu = grams/molar mass
Convert mols HNO3 to mols Cu using the coefficients in the balanced equation.
Now convert mols Cu to grams. g = mols x atomic mass.