For [Pt(NH3)(H2O)BrCl] with square planar geometry and four different ligands, geometrical isomerism arises from different positional arrangements: X = 3.
For [CrCl2(ox)2]3−, the trans isomer is optically inactive (meso compound) while cis is optically active, giving Y = 1.
For [Co(NH3)3(NO2)3] in octahedral geometry, facial (fac) and meridional (mer) isomers are possible: Z = 2.
Therefore, X + Y + Z = 3 + 1 + 2 = 6