How to find the change of heat energy

Find ΔH4 using the following information:

Zn(g) + 2HCl (aq) --> ZnCl2(aq) + H2(g) ΔH1= -188.2kJ
ZnO(g) + 2HCl(aq) --> ZnCl2(aq) + H2O ΔH2= -176.9kJ
H2(g) + 1/2 O2(g) --> H2O(l) ΔH3= -285.8kJ
Zn(g) + 1/2 O2(g) --> ZnO(g) ΔH4= ????

(A) Zn(g) + 2HCl (aq) --> ZnCl2(aq) + H2(g) ΔH1= -188.2kJ
(B) ZnO(g) + 2HCl(aq) --> ZnCl2(aq) + H2O ΔH2= -176.9kJ
(C) H2(g) + 1/2 O2(g) --> H2O(l) ΔH3= -285.8kJ

to get:
Zn(g) + 1/2 O2(g) --> ZnO(g) ΔH4= ????
we use
one equation (A) to get Zn(g) as a reactant
one equation (C) to get 1/2 O2(g) as a reactant
& the reverse of one equation (B) to get ZnO(g) as a product


i.e.
+1 (A) : Zn(g) + 2HCl (aq) --> ZnCl2(aq) + H2(g)
+1 (C): H2(g) + 1/2 O2(g) --> H2O(l)
-1 (B) ZnCl2(aq) + H2O --> ZnO(g) + 2HCl(aq) (reversed)

notice that
2HCl (aq) --> cancels with --> 2HCl (aq)
ZnCl2(aq) --> cancels with --> ZnCl2(aq)
H2(g) --> cancels with --> H2(g)
H2O(l) --> cancels with --> H2O(l)

& leaving behind only what you wished for:
Zn(g) + 1/2 O2(g) --> ZnO(g)

so
Hess's law says that if combining one equation (A) , with one equation (C) & with the reverse of one equation (B) , gives you the equation you wish,
then
combining the dH reaction of (A) , with the dH reaction of one equation (C) & with the reverse of the dH reaction of one equation (B) , gives you the dH you wish

so
dH(A) + dH(C) - dH(B) = dH reaction
(-188.2kJ) + (-285.8kJ) - ( -176.9kJ) = dH reaction

dH = -297.1 kJ

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