To solve this graphically, we need to plot the two equations:

1. $y = 2x^2 - 3x - 4$ (a quadratic equation that will form a parabola)
2. $y = 2 - 4x$ (a linear equation forming a straight line)

Steps:

1. Define the Range for $x$: We'll plot $x$ values from $-3$ to $3$.
2. Plot Both Equations: We'll graph each equation within this range.
3. Find Intersection Points: The points where the two graphs intersect will provide the values of $x$ and $y$ that satisfy both equations.

Let's plot it.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, here’s a suggestion on how you could solve this graphically yourself:

1. Plot both equations within the range of $x$ from $-3$ to $3$.
2. For the quadratic equation $y = 2x^2 - 3x - 4$, create a set of points for $x$ in the range and calculate corresponding $y$-values.
3. Similarly, for the linear equation $y = 2 - 4x$, calculate $y$-values for the same $x$-range.
4. Draw both graphs on the same axes, and identify the intersection points where both equations give the same $y$-value for the same $x$-value. These points will be your solutions.

Would you like a more detailed step-by-step on how to do this manually or any additional assistance with another part of the problem?

Here are some related questions you might be interested in:

1. How can I determine intersections between two functions algebraically?
2. How can I interpret intersections on a graph to find solutions?
3. What role does the quadratic shape play in graphical solutions?
4. How does changing the range of $x$ affect the graph and solutions?
5. How can we confirm the solutions we find graphically?

Tip: When plotting manually, check multiple values for accuracy, especially near where curves intersect.