Given: \(x \cdot y = 12\) and \(y \cdot z = 10\). To find \(x \cdot z\), we multiply both equations: \((x \cdot y) \times (y \cdot z) = 12 \times 10 = 120\). This gives us \(x \cdot y^2 \cdot z = 120\). However, we need to find the relationship. From the equations, we can derive that \(x \cdot z = \frac{(x \cdot y) \times (y \cdot z)}{y^2}\). With the pattern given, \(x \cdot z = 3 \cdot 10 = 30\).