Consder that for a function with an absolute value, the vertex is obtained for the values of x which makes the absolute term equal to zero.
In this case, for y = lx - 4l - 3, the value x = 4 makes the absolute term equal to zero.
Then, if you replace x = 4, you get:
y = l4 - 4l - 3 = 0 - 3 = -3
Hence, the point of the vertex is (4,-3), as you can see in the following image:
