In order to solve this problem we need to know two things.
1. How to put our equations into y = mx + b form and
2. What the slopes of parallel lines mean.
The reason that we need to have our equation in y = mx + b form is that from this form we can determine the slope of the line (m) and the y-intercept (b). We however are more interested in the slope which is the value in front of the variable x in the m spot.
To put our equations into y = mx + b form we must solve for the y component of the equation. Lets say we have the equation 4x + 2y = 6 and we want it into y =mx + b form.
First we have to move the x term to the other side of the equal sign using subtraction obtaining 2y = -4x + 6
Next we have to divide the y term by whatever constant is infront of the y. In this case it is 2, so we will divide every term on both sides of the equal sign by 2 obtaining
y= -2x + 3
We now have our equation in y = mx + b form. Moreover we now can determine the value of our slope to be -2 because the slope is the value infront of the x when it is written in this form.
When we are given two lines and we make the claim that they are parallel they share one common characteristic and that is that their slopes are equal. So if we have our equation from above y= -2x +3 which has a slope of -2, then the slope of a line parallel would have a slope of -2.
So make sure your equations are in y = mx + b form and remember lines that are parallel have equal slopes.
I hope this helps,