To determine if line m is parallel to side AC of triangle ABC, we can use the Converse of the Basic Proportionality Theorem (also known as Thales' Theorem). This theorem states that if a line divides two sides of a triangle proportionally, then the line is parallel to the third side.

We are given the following lengths:

• AP = 9
• BP = 6
• BQ = 8
• QC = 12

We need to check if the ratios AP/PB and BQ/QC are equal. If they are equal, then line m is parallel to AC.

Let's calculate the ratios:

• AP/PB = 9/6 = 3/2 = 1.5
• BQ/QC = 8/12 = 2/3 ≈ 0.667

Since AP/PB (1.5) is not equal to BQ/QC (2/3), line m is not parallel to side AC.