First rearrange the equations into slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
Once in that form you can easily compare the slopes. As Paul M. states previously, the equations are parallel when they have the same slope.
So for the first equation:
y - 4 = 3(x + 5)
y - 4 = 3x + 15 (distribute the 3)
y = 3x + 19 (isolate y on left side of equation to get slope-intercept form y = mx + b)
Here you can see the slope is 3.
Rearrange the other 3 equations into the slope-intercept form, and you will see why Paul M. is correct.