To solve this problem, we need to identify the number of body-centered unit cells among the 14 types of Bravais lattices.$\\$The 14 Bravais lattices are categorized based on their lattice systems and centering types.$\\$The lattice systems are:$\\$• Cubic$\\$• Tetragonal$\\$• Orthorhombic$\\$• Hexagonal$\\$• Rhombohedral$\\$• Monoclinic$\\$• Triclinic$\\$The centering types are:$\\$• Primitive (P)$\\$• Body-centered (I)$\\$• Face-centered (F)$\\$• Base-centered (C)$\\$Now, let's identify the body-centered (I) unit cells:$\\$1. Cubic system:$\\$• Body-centered cubic (bcc)$\\$2. Tetragonal system:$\\$• Body-centered tetragonal (bct)$\\$3. Orthorhombic system:$\\$• Body-centered orthorhombic (bco)$\\$These are the only body-centered unit cells among the 14 Bravais lattices.$\\$Therefore, the number of body-centered unit cells is $3. \\$This corresponds to Option 4.