Not all lines have both an x and a y-intercept.
Horizontal lines (other than the x-axis itself) have a 
y-intercept but no x-intercept.
Vertical lines (other than the y-axis itself) have an 
x-intercept but no y-intercept.

If the equation of a line contains only 1 variable, then it has only
1 intercept.  If it contains two variables, then it has two intercepts.

2y + 6 = 0 contains only ONE variable (letter), the letter y, so it
is a horizontal line with only a y-intercept and no x-intercept.

To find the y-intercept, solve it for y:

2y + 6 = 0
    2y = -6
     y = -3

So it is a horizontal line with a y-intercept on the y-axis at y=-3.  It
has no x-intercept.

Here is the graph



Edwin