First write a balanced chemical equation to show the reaction

  Mg +  2HCl →  MgCl\(_2\)  +  H\(_2\)

 1mole  :  2 moles

From what we were given  n = \(\frac{CV}{1000}\)

 n = \(\frac{{0.5}\times{260}}{1000}\)

 n = 0.13 mole

By Simple proportion,

 1 mole of Mg → 2 moles of HCl

  then  x mole of Mg → 0.13mole of HCl

 x = \(\frac{0.13}{2}\) = 0.065mole

Also recall that  n = \(\frac{m}{M}\)

 m = n x M

 m = 0.065 x 24 = 1.56g

Therefore the mass of Magnesium required to react with 260cm3 of 0.5 M HCl is 1.56g