Step 1: Linkage isomerism arises only when the complex contains an ambidentate ligand, i.e. a ligand that can attach to the central metal through two different donor atoms. Common ambidentate ligands are \( NO_2^- \) (through N as nitro or through O as nitrito), \( SCN^- \) and \( CN^- \).
Step 2: Examine each complex for an ambidentate ligand:
(i) \( [Cr(NH_3)_4Cl_2] \): ligands are \( NH_3 \) and \( Cl^- \), neither is ambidentate. No linkage isomerism.
(ii) \( [Co(NH_3)_5(NO_2)]Cl_2 \): contains \( NO_2 \), which can bind as nitro (\( -NO_2 \), through N) or nitrito (\( -ONO \), through O). This gives linkage isomers.
(iii) \( [Co(NH_3)_5(SO_4)]Br \): sulphate binds through O and, with a free \( Br^- \) outside, shows ionisation isomerism, not linkage isomerism.
(iv) \( [Pt(NH_3)_2Br_2] \): only \( NH_3 \) and \( Br^- \); no ambidentate ligand.
Step 3: Only option (ii) has the ambidentate \( NO_2 \) ligand, so it alone shows linkage isomerism.
\[\boxed{[Co(NH_3)_5(NO_2)]Cl_2}\]