Bond energies.

Step 1 of 6

Breaking and making

Zoom to the molecules is at Molecules: a slice through the flame that shows the molecules themselves. Methane ($\mathrm{CH_4}$⁠) and oxygen ($\mathrm{O_2}$⁠) go in, and carbon dioxide ($\mathrm{CO_2}$⁠) and water ($\mathrm{H_2O}$⁠) come out. For that to happen, every bond in the reactants has to break, and every bond in the products has to form.

Step 2 of 6

The bonds that break

Every chemical bond holds a certain energy: the bond energy is the energy it takes to break a mole of such bonds. A double bond is stronger than a single bond between the same atoms. Count every bond in the reactants: each molecule, times its coefficient.

Step 3 of 6

The bonds that form

When a bond forms, it releases exactly the energy it takes to break it. Now count the bonds in the products.

Step 4 of 6

The difference

The reaction’s $\Delta H$⁠ is what went in minus what came out:

$\Delta H = \sum E(\text{bonds broken}) - \sum E(\text{bonds made})$$\Delta H =$$\sum E(\text{bonds broken}) - \sum E(\text{bonds made})$⁠

If the new bonds are stronger than the old ones, more comes out than went in, and $\Delta H$⁠ is negative: the reaction is exothermic.

Step 5 of 6

Averages

The flame in the Scene gives out 802 kJ per mole of methane, the measured value. Your calculation is close to it, but not exact.

Step 6 of 6

Another reaction

The same method works for any reaction in the gas, even when there is no flame to compare with.