To find the value of $H$, we will solve the system of equations step by step.

From the given equations, we will first focus on equations that directly involve $H$. Let's rewrite them for clarity:

1. $A + H = 120$
2. $B + H = 129$
3. $C + H = 138$
4. $D + H = 111$
5. $E + H = 147$
6. $F + H = 102$
7. $G + H = 132$
8. $H + A = 120$ (This is the same as equation 1, so it does not add new information.)

Since the equations involve different variables (A, B, C, etc.), we need more relationships between these variables to isolate $H$.

Looking at the structure, equation (1) $A + H = 120$ and equation (8) $H + A = 120$ indicate the same equation. If we had values for any of the other variables (A, B, C, etc.), we could solve for $H$.

Is there any additional information on these variables, or should we solve in terms of a specific variable?

Once clarified, I can give a more concrete solution!