Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.1 Finding Limits Using Tables and Graphs - 13.1 Assess Your Understanding - Page 896: 22

The limit does not exist.

As we can see as $x$ gets closer and closer to $4$ from the left, the value of the function (the y-value) gets closer and closer to $4$. But, as we can see as $x$ gets closer and closer to $4$ from the right, the value of the function (the y-value) gets closer and closer to $2$. Thus the limits from the two sides differ, thus the limit does not exist.