I guess your two equations are:
Since the plus (+) and equals (=) signs have been stripped from your question.
If this is the case, then they are not parallel since their gradients are not the same.
Without working them out exactly, it can be seen that one is positive (equation 1.) and the other is negative (equation 2.):
If you mean: 2x+3y = 12 then y = -2/3x+4 whereas -2/3 is the slope and 4 is the y intercept
[ y = -2x + any other number ] is parallel to [ y = -2x + 6 ].
If you mean: 2x+4y = 6 then 2x+4y = 12 is parallel to it because parallel lines retain the same slope but have different y intercepts
y = 2x
If you mean: 6x+3y = 12 then it is y = -2x+4 in slope-intercept form
Batteries in series supply 2x the voltage. Batteries in parallel provide 2x the current.
Any line which has a gradient which is not 2 will not be parallel to the line y = 2x + 1.
If you mean: 6x-3y = 12 Then: -3y = -6x+12 And: y = 2x-4 So: the slope is 2 and the y intercept is -4
If the second equation is: y minus 2x equals 3, then:y - 2x = 3 ⇒ y = 2x + 3 and it is parallel to y = 2x.Otherwise (with with missing operator as "plus", "multiply" or "divide"), the lines are neither parallel nor perpendicular.