You follow a systematic procedure to balance the equation.
The other product is calcium hydroxide.
Start by converting the words to a chemical equation.:
#"CaC"_2 + "H"_2"O" → "C"_2"H"_2 + "Ca(OH)"_2#
A method that often works is first to balance everything other than #"O"# and #"H"#, then balance #"O"#, and finally balance #"H"#.
Another useful procedure is to start with what looks like the most complicated formula.
The most complicated formula looks like #"Ca(OH)"_2#. We put a 1 in front of it to remind ourselves that the number is now fixed.
#"CaC"_2 + "H"_2"O" → "C"_2"H"_2 + color(red)(1)"Ca(OH)"_2#
Balance #"Ca"#:
We have #"1 Ca"# on the right, so we need #"1 Ca"# on the left. We put a 1 in front of the #"CaC"_2#.
#color(orange)(1)"CaC"_2 + "H"_2"O" → "C"_2"H"_2 + color(red)(1)"Ca(OH)"_2#
Balance #"C"#:
We have fixed #"2 C"# on the left. We need #"2 C"# on the right. Put a 1 in front of #"C"_2"H"_2#.
#color(orange)(1)"CaC"_2 + "H"_2"O" → color(blue)(1)"C"_2"H"_2 + color(red)(1)"Ca(OH)"_2#
Balance #"O"#:
We have fixed #"2 O"# on the right. We need #"2 O"# on the left. Put a 2 in front of #"H"_2"O"#.
#color(orange)(1)"CaC"_2 + color(purple)(2)"H"_2"O" → color(blue)(1)"C"_2"H"_2 + color(red)(1)"Ca(OH)"_2#
Every formula now has a coefficient. We should have a balanced equation.
Let's check.
#bb("Atom" color(white)(m)"lhs"color(white)(m)"rhs")#
#color(white)(m)"Ca"color(white)(mml)1color(white)(mml)1#
#color(white)(m)"C"color(white)(mmm)2color(white)(mml)2#
#color(white)(m)"H"color(white)(mmm)4color(white)(mml)4#
#color(white)(m)"O"color(white)(mmm)2color(white)(mml)2#
All atoms balance. The balanced equation is
#"CaC"_2 + "2H"_2"O" → "C"_2"H"_2 + "Ca(OH)"_2#
