A 38.0mL solution 0.026M solution of HCl reacts with a 0.032M NaOH.
a)calculate the number of moles of HCl originally present.
b)how many moles of NaOH are needed to neutralize the acid?
c)calculate the volume of the NaOH required to react completely with the acid
d)write a balanced chemical reaction for above process

Actually, the equation of the reaction is what helps you in finding how many moles of that or that reagent needed. I would advise you to therefore write the equation first.

a) That should be easy. Do it by proportions:

0.026 solution = 0.026 mol in 1000 mL

1000 mL -> 0.026 mol of acid
1 mL -> 0.026/1000 mol
38 mL -> (0.026/1000) * 38 mol

b) Using your equation, you'll have the molar ratio of the reagents required. You'll see that one mole of acid reacts with one mole of alkali.

So, (0.026/1000) * 38 mol of acid will react with how many moles of alkali?

c) Use proportions again:

1000 mL -> 0.032 mol of alkali.
0.032 mol -> 1000 mL
1 mol -> 1000/0.032 mL

Now, find for the number of moles of alkali you need, using the amount of moles you got in b)

d) You already did that from the start, as I advised you.