Question

Y=|x-2|-4 how do I solve this and graph it

Answer 1

Nothing to "solve" here.  Just graph this absolute value function.

Note that if x=2 we get y = -4.  Thus, (2,-4) is the vertex.  Plot this point.

Now, starting from (2, -4), draw a line at a 45 degree angle to the horizontal.

Then draw a corresponding line on the other side of the y-axis.  You're done!