1. **State the problem:** Find the equation of the straight line passing through the point $(4,14)$ with gradient $2$. 2. **Recall the formula:** The equation of a straight line is given by $$y = mx + c$$ where $m$ is the gradient and $c$ is the y-intercept. 3. **Use the given gradient:** Here, $m = 2$. 4. **Substitute the point $(x, y) = (4, 14)$ into the equation to find $c$:** $$14 = 2 \times 4 + c$$ $$14 = 8 + c$$ 5. **Solve for $c$:** $$c = 14 - 8$$ $$c = 6$$ 6. **Write the final equation:** $$y = 2x + 6$$ This matches the option $y = 2x + 6$. **Answer:** The equation of the line is $y = 2x + 6$.