Explanation:
To determine the number of stereoisomers of the given compound, we need to analyze the different stereocenters present in the compound and the possible arrangements of substituents around each stereocenter.

Identify the stereocenters:
A stereocenter is an atom in a molecule where the interchange of two groups produces a different stereoisomer. In the given compound, the carbon atom connected to the bromine (C) and the carbon atom connected to the hydroxyl group (C') are stereocenters.

Analysis of stereocenters:
In the compound (CH3)2CHCH = CHCH2CH(OH)CH2Br, the C and C' atoms have four different substituents attached to them. Let's label each substituent as follows:
- For the C atom: A, B, X, Y
- For the C' atom: P, Q, R, S

Arrangements around the stereocenters:
The possible arrangements of substituents around the C atom and the C' atom are as follows:

For the C atom:
- A, B, X, Y (original arrangement)
- A, B, Y, X (enantiomer)

For the C' atom:
- P, Q, R, S (original arrangement)
- P, Q, S, R (enantiomer)

Combining the arrangements:
To determine the number of stereoisomers, we need to combine the arrangements at the C atom and the C' atom. Since there are two arrangements at each stereocenter, we multiply the number of arrangements together.

Number of stereoisomers = Number of arrangements at C atom × Number of arrangements at C' atom
Number of stereoisomers = 2 × 2 = 4

Therefore, there are 4 stereoisomers possible for the given compound.
The correct answer is option 'C'.