A 250.0 mL buffer solution initially contains 2.5×10^2 M of HCHO2 and 2.5×10^2 M of NaCHO2.?

As far as I can see there is something missing from your question:
You state that you have 250mL of a buffer solution containing HCOOH and HCOONa in equal molar quantities.
It is comparatively simple to work out that pH of buffer = pKa HCOOH.
This is pKa = 3.77 , therefore pH = 3.77
Incidentally I do not believe that you have a 2.5*10^2M solution. This is 250M which is impossible. Probably 2.5*10^-2M is more realistic.

Then you ask “What mass of the correct reagent should you add?
(the reagent is NaOH) ? please help.

I now ask – what is this correct mass of NaOH supposed to do?
Generally these questions are worded: What mass of NaOH must be added to this buffer in order to increase the pH to 4.50, as an example.
I believe that you have missed out on the complete question.
The calculation done in the first answer, and which you say you have obtained the same answer, is not what the question wants. You are not being asked for the mass of HCOOH and HCOONa to produce the specified buffer, but how much NaOH must be added to the buffer in order to change the pH to some specified value. The question asks only for the mass of NaOH – not the HCOOH.
Please reread the question and supply the missing information.

The reagent NaOH reacts with HCHO₂ to give NaCHO₂.
HCHO₂ + NaOH → NaCHO₂ + H₂O

Number of moles of NaCHO₂ formed = (2.5 × 10⁻²) × (250/1000) = 6.25 × 10⁻³ mol

Refer to the equation. 1 mole of NaOH gives 1 mole of NaCHO₂.
Number of moles of NaOH needed = 6.25 × 10⁻³ mol

Molar mass of NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol
Mass of NaOH needed = 40.00 × (6.25 × 10⁻³) = 0.25 g

thank cant be it because i already got that answer and its wrong