How many ml of 0.100 m naoh is needed to titrate 20.0 ml of 0.100 m h2so4

So the first thing we must do is write a balanced equation for the reaction and we know the equation is balnced when all the species on the RHS is equal to the species on the LHS
                      2NaOH  +  H₂SO₄   →  Na₂SO₄  +  2H₂O

So now it's time to identify what you know from the question (volume & conc. of H₂SO₄) and use that info to find the unknown (volume of NaOH)

If 1000 ml  of H₂SO₄ contain 0.100 mol   [0.100 M is the amount of moles in
                                                                 1 L (1000 ml)]
then let 20 ml of H₂SO₄ contain x mol     [20 ml is the amount of the acid that                                                                   took place in the reaction]
    
⇒  x  =  
       
         = 0.002 mol

Mole ratio of NaOH  to  H₂SO₄  can be obtained from the balanced equation
        2NaOH  +  1H₂SO₄   →  Na₂SO₄  +  2H₂O

  thus mole ratio of   NaOH  to  H₂SO₄  is 2 : 1

∴ if mole of of H₂SO₄  =  0.002 mol
  then moles of NaOH = (0.002 mol) × 2
                                    = 0.004 mol

Now molarity = 
    ∴ by transposition

       Volume = 
                    = 
                    = 0.04 L
                    = 40 mL

Yes she is correct. the answer is completely correct