Hey there!!
Parallel lines have the same slope. If they have different slope, then they are not parallel because both lines would combine at some point.
The y-intercept form:
y = mx + b
In this equation, 'm' is considered to be the slope.
The equation we have is 6y = -2x + 4
First, let's divide all the sides with 6 to isolate the value of 'y'.
... 6y = -2x + 4
... y = -1/3x + 2/3
The slope is -1/3...
... hence the slope in the other equation should be -1/3.
Equation we got...
... 2y = ax - 5
Let's divide by 2 on both sides...
... y = ax/2 - 5
The slope in this a/2
Hence, ...
... a/2 = -1/3
... 3a = -2
... a = -2/3
Hence, the value of a is -2/3.
Hope my answer helps!