Let, the mass of \(BaCl_2\) be \(x~\text{g}\)
According to the equation,
\(\underset{x~\text{g}}{BaCl_2}+\underset{24.4~\text{g}}{Na_2SO_4}\to\underset{46.6~\text{g}}{ BaSO_4}+\underset{23.4~\text{g}}{2NaCl}\)
According to law of conservation of mass,
\(\text{Total mass of reactants=Total mass of products}...(i)\)
\(\text{Total mass of reactants=(x+24.4) g}\)
\(\text{Total mass of products=(46.6+23.4) g}\)
Substituting in equation \((i)\)
\(x+24.4=46.6+23.4\\
x=46.6+23.4-24.4\\
\Rightarrow x=45.6~\text{g}\)
Hence, the weight of \(BaCl_2\) is \(45.6~\text{g}\).