Which of the following inequalities is represented by the shaded region on the coordinate plane above?

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We first need to identify the line that divides the two regions.

As shown above, the $y$-intercept is $(0,4)$ and the slope is $-\dfrac{4}{2}=-2$.

$$y=-2x+4 \tag*{\tiny equation of line}$$

Since the region above the line is shaded, we need to use the greater than sign. A dotted line means we use $\gt$ rather than $\geq$.

$$\boxed{y\gt-2x+4}$$

Since we are given the inequalities in the answer choices, we can test an arbitrary solution. Since the line is dashed, solutions on the line are not valid which means that the inequality sign must be $\lt$ or $\gt$.

For example, let's test this point below. It is in the shaded solution region so it must satisfy the inequality.