(i) The lower dotted line is the elements in their standard states, i.e. Mg
(s) + Br
2(l)
The upper dotted line is Mg
2+(g) + 2Br(g)
(ii)
You need the enthalpy of hydration of bromide ions, i.e. Br
-(g) ==> Br
-(aq)
There is no lattice enthalpy step in the cycle.
You do need to add up (magnitude) all of the LHS and it should equal all of the RHS (just one way to do it.
The other way is to go around the cycle in the other direction to the step that you are trying to determine (bottom right)
186 + 525 + 2(112) + 148 + 736 + 1450 = (2 x dH(hydration) Br-) + 1926 + (2 x 325)
Rearrange
(2 x dH(hydration) Br-) = 693
Hydration enthalpy of bromide ions = -346.5 kJ (hydration is always exothermic)