1.513g of monoprotic acid (HX) is dissolved in water, and the volume is 250.0 ml after the dissolving. The solution was then titrated 38.12g of .100 M NaOH to reach the end point of the titration. What is the molecular weight of HX?

I assume you meant 38.12 mL and not g.

mols NaOH = M x L = ?
mols monoprotic HA = same.
M HA = mols HA/L HA
mol HA = grams/molar mass. You have mols and grams, solve for molar mass.