200. ml of a 0.50 m naoh solution requires 100.0 ml of a hcl solution to
neutralize it. what is the concentration of the hcl solution?

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
                      NaOH  +  HCl   →  NaCl  +  H₂O

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

If  1L (1000ml) of NaOH contains 0.50 moles then

let 200ml of NaOH contain x moles

⇒ x = 

       =  0.1 mol

∴ moles of NaOH that reacted with HCl is 0.1 mol

Now mole ratio of NaOH : HCl based on the balance equation is 1 : 1
                   1NaOH  +  1HCl   →  NaCl  +  H₂O

∴ if moles of  NaOh = 0.1 mol
  then moles of HCl = 0.1 mol

<<Alright Now to find the molarity of HCl>>

If 0.1 moles of HCl (which was what took place in the reaction) is in 100 ml
then let  x moles would be in 1000ml (1L)

∴ x = 
      =  1 mol

Thus the concentration of the HCl solution is 1 mol/L 

PS. what is in bold is what you really need, the rest is just to help in understanding.