How to calculate lattice energy of magnesium sulfide?

Take the second equation and flip it around. This changes the sign of ΔH°

Mg2+(g) + 2e- → Mg(g) ΔH°=-2186 KJ/mol

flip the fourth equation around. Again only the sign of ΔH° changes

S2-(g) → S(g) + 2e- ΔH°=-450 KJ/mol

Divide the fifth equation by 8. This also divides the value of ΔH° by 8

Mg(s) + 1/8S8(s) → MgS(s) ΔH°=-343 KJ/mol

flip the first equation

Mg(g) → Mg(s) ΔH°=-148 KJ/mol

flip the third equation and divide by 8

S(g) → 1/8S8(s) ΔH°=-279 KJ/mol

Now combine all the equations and you should get the desired equation. Add all the values for ΔH° and you get the lattice energy for MgS.

Mg2+(g) + S2-(g) → MgS(s) ΔH°MgS=-3406 KJ/mol