Hey, so here's the way I approached this problem. I started by writing out the reactions. Then, I knew that the C(graphite), in the 3rd reaction had to be on the right hand side, so I reversed that equation. Remember that reversing an equation, we reverse delta H.
At this point we're at the following:
1) C(diamond) + O2 (g) ------> CO2 (g) Delta H = -395.4
2) 2 CO2 (g) --------> 2 CO (g) + O2 (g) Delta H = 566.0
3) CO2 (g) -------> C(graphite) + O2 (g) Delta H = 393.5
4) 2CO (g) ------> C(graphite) + CO2 (g) Delta H = -172.5
So, now let's count up the molecules on each of the reaction:
Starting Materials:
1 - C(diamond)
1 - O2
3 - CO2
2 - CO
0 - C(graphite)
Products:
0 - C(diamond)
2 - O2
2 - CO2
2 - CO
2 - C(graphite)
We know that once everything cancels, we should be left with equal moles of C(diamond) and C(graphite). If we know that, then we see we need to gain: 1 C(diamond) and 1 O2 on the reactants side and 1 CO2 on the products side.
Can you go from there to figure it out?