The given chemical equation is:
\[
\mathrm{Jg}_{4} 4 \mathrm{AlC}_{3} + \mathrm{NaOH} = \mathrm{AlOH}_{3} + \mathrm{NaCl}
\]
Step 2: Correct the Chemical Equation
The given equation appears to be incorrect or incomplete. Let's correct it based on common chemical reactions. Aluminum carbide (\(\mathrm{Al_4C_3}\)) reacts with sodium hydroxide (\(\mathrm{NaOH}\)) to form aluminum hydroxide (\(\mathrm{Al(OH)_3}\)) and sodium chloride (\(\mathrm{NaCl}\)).
The corrected equation should be:
\[
\mathrm{Al_4C_3} + \mathrm{NaOH} + \mathrm{H_2O} \rightarrow \mathrm{Al(OH)_3} + \mathrm{CH_4} + \mathrm{NaCl}
\]
Step 3: Balance the Chemical Equation
To balance the equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation.
Aluminum (Al): There are 4 Al atoms on the left side, so we need 4 Al atoms on the right side.
Carbon (C): There are 3 C atoms on the left side, so we need 3 C atoms on the right side.
Sodium (Na): We need to balance Na atoms.
Oxygen (O) and Hydrogen (H): We need to balance these atoms considering the water and hydroxide ions.