To determine the empirical formula of compound $X,$ we need to find the mole ratio of elements A, B, and C.$\\$Given percentages:$\\$• A: $32\% \\$• B: $20\% \\$• C: $100\% - (32\% + 20\%) = 48\% \\$Given atomic masses:$\\$• A: $64 \,$u$\\$• B: $40 \,$u$\\$• C: $32 \,$u$\\$Calculate the number of moles of each element in 100 g of the compound:$\\$Moles of A:$\\ \frac{32}{64} = 0.5 \\$Moles of B:$\\ \frac{20}{40} = 0.5 \\$Moles of C:$\\ \frac{48}{32} = 1.5 \\$Now, find the simplest whole number ratio of moles:$\\$Divide each by the smallest number of moles (0.5):$\\$• A: $\frac{0.5}{0.5} = 1 \\$• B: $\frac{0.5}{0.5} = 1 \\$• C: $\frac{1.5}{0.5} = 3 \\$Thus, the empirical formula is $ABC_3. \\$Therefore, the correct option is Option 4: $ABC_3.$