The parametric equation for a line passing through two points is
p = p1 + t(p2 - p1)
where t is in [0,1].
Since we have x = -5 - 4t, y = 1 - t, z = 3 + 2t, we get
p1 = (-5, 1, 3), p2 = (-9, 0, 5) and p2 - p1 = (-4, -1, 2) = A
where A is the direction vector of the line.
Given the plane equation x + 2y + 3z -9 = 0 or x + 2y + 3z = 9, this is in the form
X dot N = P dot N so that the normal to the plane is N = (1,2,3).
The line and plane defined above are parallel if the dot product of N and A is equal to zero. In other words the normal to the plane and the line direction vector are perpendicular to each other. Taking the dot product, we get
N dot A = 1*(-4) + 2*(-1) + 3*2 = -4 - 2 + 6 = 0
Therefore the line and plane defined above are parallel!