how many grams of KOH are needed to make 590 ml of a solution with a pH of 11.35?

Not really organic chem!

First calculate [OH-]

if pH=11.35 then pOH= 14-11.35 = 2.65

if pOH=2.65 then [OH-]=0.002239 mol L^-1

so solution contains
590 x 0.002239 mmole = 1.32 mmole

or 0.00132 mole

1 mole of KOH gives 1 mole of OH- in solution

molar mass of KOH = 56.1

so mass of KOH needed = 0.00132 x 56.1 = 0.074 g

but check the maths!