\(n_{KOH}=a\left(mol\right)\)
\(n_{H_2}=\dfrac{0.672}{22.4}=0.03\left(mol\right)\)
\(n_{H_2O}=\dfrac{1}{2}n_{KOH}+n_{Ca\left(OH\right)_2}+2n_{H_2}=0.5a+0.01+2\cdot0.03=0.5a+0.07\left(mol\right)\)
\(BTKL:\)
\(m_X+m_{H_2O}=m_{Ca\left(OH\right)_2}+m_{KOH}+m_{H_2}\)
\(\Rightarrow2.43+\left(0.5a+0.07\right)\cdot18=0.01\cdot74+56a+0.03\cdot2\)
\(\Rightarrow a=0.06\)
\(m_{KOH}=0.06\cdot56=3.36\left(g\right)\)