Lattice energy of $\mathrm{NaCl}$ is ' X '. If the ionic size of ${\mathrm{A}}^{+2}$ is equal to that of ${\mathrm{Na}}^{+}$and ${\mathrm{B}}^{-2}$ is equal to ${\mathrm{Cl}}^{-}$, then lattice energy associated with the crystal AB is

 The lattice energy of crystal AB is 4X.
In a compound, the energy associated to the crystal lattice is lattice energy. Mathematically,
${\mathrm{E}}_{\text{lattice }}=\mathrm{k}\frac{{\mathrm{Q}}_1{\mathrm{Q}}_2}{ \mathrm{d}}$ =X
where, k = proportionality constant
${\mathrm{Q}}_1$ and ${\mathrm{Q}}_2$ are the charges on the ions in coulombs.
$\mathrm{d}=$ distance between the ion charges.
Lattice energy of $\mathrm{NaCl}=\mathrm{X}$
${\mathrm{E}}_{\text{lattice }}\left(\mathrm{NaCl}\right)=\frac{2{\mathrm{Q}}_{1}2{\mathrm{Q}}_2}{ \mathrm{d}}=4\mathrm{X}$