Is the system of equations is consistent, consistent and coincident, or inconsistent?

y=−12x+3
y=4x+2

Consistent means they are intersecting at one point only. Consistent and Coincident means that they are the same line and intersect at infinitely many points. An inconsistent system means the two lines never intersect (since they are parallel).
Your system is Consistent as, looking at the slopes which are -12 and 4, the lines cannot possibly be the same lines nor can they be parallel.