Here, I use \mathllap on the last line. But as you can see, there is still one remaining margin issue that you need to consider.
Also, the \end{alignat} does not take an argument.
\documentclass{article} \usepackage[pass,showframe]{geometry} \usepackage{mathtools} \usepackage{mhchem} \usepackage{amssymb} \begin{document} Overall formation of ethane thingy: \ce{2 C(s) + 3 H2(g) -> C2H6(g)} \\ \begin{alignat}{2} \ce{2C(s) + 2O2(g) &-> 2CO2(g)} &\Delta H &= -786 kJ\\ \ce{3H2(g) + 3/2 O2(g) &-> H2O(l)} &\Delta H &= -858 kJ\\ \ce{2 CO2(g) + 3 H2O(l) &-> C2H6(g) + 7/2 O2 (g)} &\Delta H &= 1560 kJ\\ \nonumber \ce{2 C(s) + 3 H2(g) + 7/2 O2(g) &-> C2H6(g) + 7/2 O2(g)} &\indent \Delta H &= -786-858+1560\\ \nonumber & &&= -84 kJ \\ \nonumber &&\mathllap{\therefore \Delta H_{f(C_2H6)}^0} &= -84kJ \end{alignat} \end{document}

You could try to break up the remaining long line, but there may be other approaches, too...
I also made your kJ units upright, though, as marmot points out, the siunitx package is tailor made for applying units to quantities.
\documentclass{article} \usepackage[pass,showframe]{geometry} \usepackage{mathtools} \usepackage{mhchem} \usepackage{amssymb} \begin{document} Overall formation of ethane thingy: \ce{2 C(s) + 3 H2(g) -> C2H6(g)} \\ \begin{alignat}{2} \ce{2C(s) + 2O2(g) &-> 2CO2(g)} &\Delta H &= -786 \mathrm{\,kJ}\\ \ce{3H2(g) + 3/2 O2(g) &-> H2O(l)} &\Delta H &= -858 \mathrm{\,kJ}\\ \ce{2 CO2(g) + 3 H2O(l) &-> C2H6(g) + 7/2 O2 (g)} &\Delta H &= 1560 \mathrm{\,kJ}\\ \nonumber \ce{2 C(s) + 3 H2(g) + 7/2 O2(g) &-> C2H6(g) + 7/2 O2(g)} &\indent \Delta H &= -786-858\\\nonumber&&&\phantom{{}={}}+1560\\ \nonumber & &&= -84 \mathrm{\,kJ} \\ \nonumber &&\mathllap{\therefore \Delta H_{f(C_2H6)}^0} &= -84\mathrm{\,kJ} \end{alignat} \end{document}

H_{f(C_2H6)}^0is wrong on several levels: subscript f should be upright, subscript formula should be upright (use\ce), superscript is not a 0, but\circ. IUPAC recommendation (Green Book) is to write\Delta_{\mathrm{f}}H^\circ (\ce{C2H6}). Lastly, are you sure about your calculation? Unit of standard enthalpy is not kJ.