Final answer:
The equation provided in the question appears to contain a typo and cannot be proved with the information given. In arithmetic progression problems, one would use established sum formulas to find relationships between different segments of the sequence, not the algebraic expression provided.
Step-by-step explanation:
The content loaded specifies that a given arithmetic progression (AP) consists of 3m terms with the sum of the first m terms being x, the next m terms being y, and the last m terms being z. The question requires proving the equation ((x - 2) = 4(y - xz)). However, there is a typo in this equation since it is not algebraically sound or relevant to the context given. Arithmetic progression problems typically involve the use of standard formulas for the sum of terms in an AP and manipulations related to sequences. Since the question's equation seems incorrect, it is not possible to provide a proof for it. Instead, typically, for an arithmetic progression problem, one would expect to establish a relationship between the sums of different segments of the series based on the common difference, the number of terms, and the first term of the sequences.