The complex(es) which can exhibit the type of isomerism shown by [Pt(NH₃)₂Br₂] is(are):

The correct options are [Pt(NH₃)₂Cl₄] and [Cr(en)₂(H₂O)(SO₄)]⁺.

Step 1: Identify the type of isomerism in the reference complex

The given complex is [Pt(NH₃)₂Br₂].

In this complex, Platinum (Pt²⁺) has a coordination number of 4 and adopts a square planar geometry. A square planar complex of the type ${\text{MA}}_2{\text{B}}_2$ exhibits geometrical isomerism (specifically cis-trans isomerism):

1. cis-isomer: The identical ligands (e.g., NH₃ or Br) are adjacent to each other (90° apart).

2. trans-isomer: The identical ligands are opposite to each other (180° apart).

Therefore, the reference complex exhibits geometrical isomerism (cis-trans isomerism).

Step 2: Analyze each given option for geometrical isomerism

Option 1: [Pt(en)(SCN)₂]

Here, 'en' (ethylenediamine) is a bidentate ligand. Because the two coordinating donor atoms of 'en' must attach to adjacent (cis) positions in a square planar complex, the two SCN^- ligands are restricted to being cis to each other. Consequently, a trans isomer cannot form without breaking the ring constraint of ethylenediamine. Thus, this complex does NOT exhibit cis-trans geometrical isomerism.

Option 2: [Zn(NH₃)₂Cl₂]

Zinc (Zn²⁺) forms a 4-coordinate complex with an sp³ hybridized tetrahedral geometry. In a symmetrical tetrahedral complex of type ${\text{MA}}_2{\text{B}}_2$, all positions are adjacent and equivalent relative to one another (bond angle is ~109.5°). Thus, geometrical isomerism is NOT possible for tetrahedral complexes.

Option 3: [Pt(NH₃)₂Cl₄]

This is an octahedral complex of Platinum (Pt⁴⁺) with coordination number 6, conforming to the formula type ${\text{MA}}_2{\text{B}}_4$.

This complex exhibits geometrical isomerism:

- cis-isomer: The two NH₃ ligands occupy adjacent positions (at a 90° angle).

- trans-isomer: The two NH₃ ligands occupy opposite positions across the metal center (at a 180° angle).

Hence, [Pt(NH₃)₂Cl₄] exhibits geometrical isomerism.

Option 4: [Cr(en)₂(H₂O)(SO₄)]⁺

This is an octahedral complex of Chromium (Cr³⁺) with coordination number 6, corresponding to the general type ${\text{M(M-M)}}_2\text{AB}$ (where 'en' is a symmetrical bidentate ligand, and H₂O and SO₄^{2- are monodentate ligands).}

It exhibits geometrical isomerism based on the positions of the monodentate ligands H₂O and SO₄^2-:

- cis-isomer: The H₂O and SO₄^2- ligands are adjacent (90° apart).

- trans-isomer: The H₂O and SO₄^2- ligands are opposite each other (180° apart).

Hence, [Cr(en)₂(H₂O)(SO₄)]⁺ exhibits geometrical isomerism.

Conclusion:

Both [Pt(NH₃)₂Cl₄] and [Cr(en)₂(H₂O)(SO₄)]⁺ exhibit geometrical isomerism, the same type of isomerism shown by [Pt(NH₃)₂Br₂].