This is a piecewise linear function with two different appearing halves.
The changeover from the first piece (x-2) to the second piece (3x+2) occurs at x= -2.
First, graph y = x-2, but instead of letting x get very large, stop and place a dark (solid) dot at (-2, 4).
Next, graph y = 3x+2, but instead of starting this graph at the extreme left, put an open circle at (-2,-2) and draw the line y = 3x+2 from there, starting at your open circle.
Bonus: because the y values of the two linear functions are different at x= -2, the overall graph is "broken" at x = -2, and we say "the graph is discontinuous at x =-2."