can someone please explain to me the correct way to solve this chemistry question?

The question is on the dilute of a solution.
The mathematic formula used is C₁V₁ = C₂V₂ where C₁ has the same unit with C₂ and V₁ has the same unit with V₂.

Stock solution: C₁ = 2 M, V₁ = ? mL
Diluted solution: C₂ = 0.5 M, V₂ = 500 mL

C₁V₁ = C₂V₂
Volume of stock solution needed, V₁ = V₂ × (C₂/C₁) = (500 mL) × (0.5/2) = 125 mL

Know this equation: it’ll save your ass in chemistry class more than you’ll ever know.

M1V1 = M2V2 (the numbers are subscripts). A variation is C1V1 = C2V2 (again the numbers are subscripts).

M1 = original concentration
V1 = volume you need to dilute to get the second concentration
M2 = the new concentration you want
V2 = the final volume you want

Knowing all that, just plug the numbers:
(2M)(V1) = (.5M)(.5L)
V1 = .25/2
V1 = .125 L or 125 ml of the original 2M

moles required is = 0.5 x 500 / 1000 = 0.5/2 = 0.25 moles.
So in 2M sol; 2 moles in one litre (1000 mL) you need to decant 2 / 0.25 = 1/8 moles
1/8 moles is contained in 25mL
Having taken 25 mL then slowly dissolve in say 300 mL .
Then finally add sufficient solvent to make up to 500mL .