1. The problem asks to find the slope of the line passing through the points $(0,4)$ and $(0,6)$. 2. The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ 3. Substitute the given points into the formula: $$m=\frac{6 - 4}{0 - 0} = \frac{2}{0}$$ 4. Division by zero is undefined in mathematics, so the slope is undefined. 5. This means the line is vertical, as both points have the same $x$-coordinate. **Final answer:** The slope of the line is \textbf{undefined}.