The coordination compound [Pt(py)(NH3)BrCl] consists of a platinum (Pt) ion coordinated to pyridine (py), ammonia (NH3), bromide (Br), and chloride (Cl) ligands. To determine the number of possible isomers for this compound, we need to consider different possible arrangements of these ligands around the central platinum ion.

1. Identify the ligands:
- pyridine (py)
- ammonia (NH3)
- bromide (Br)
- chloride (Cl)

2. Determine the coordination number:
The coordination number is the total number of ligands attached to the central metal ion. In this case, there are a total of 4 ligands attached to the platinum ion, so the coordination number is 4.

3. Consider the possible arrangements:
Since the coordination number is 4, we can have four different ligands in different positions around the platinum ion. Let's consider each ligand separately and determine the number of possible positions for each:

- pyridine (py):
The pyridine ligand can be located in three different positions: cis to the ammonia ligand, trans to the ammonia ligand, or trans to both bromide and chloride ligands.

- ammonia (NH3):
The ammonia ligand can be located in three different positions: cis to the pyridine ligand, trans to the pyridine ligand, or trans to both bromide and chloride ligands.

- bromide (Br) and chloride (Cl):
The bromide and chloride ligands can be located in two different positions: cis or trans to both the pyridine and ammonia ligands.

4. Multiply the possibilities:
To determine the total number of possible isomers, we multiply the number of possibilities for each ligand position. In this case, we have 3 possibilities for the pyridine ligand, 3 possibilities for the ammonia ligand, and 2 possibilities for both bromide and chloride ligands.

Total number of possible isomers = 3 × 3 × 2 × 2 = 36

Therefore, the number of possible isomers for [Pt(py)(NH3)BrCl] is 36.