Y=5a-3b
Y=5(12)-3(4)
Y=60-12
Y=48
You don't have a sign between b and c in the equation, so I cannot help you with the last operation
Take the homogeneous part and find the roots to the characteristic equation:

This means the characteristic solution is

.
Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form

. Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.
With

and

, you're looking for a particular solution of the form

. The functions

satisfy


where

is the Wronskian determinant of the two characteristic solutions.

So you have




So you end up with a solution

but since

is already accounted for in the characteristic solution, the particular solution is then

so that the general solution is
Yes because if you distribute the 3 and multiply it with 3 • x and 3• 6 you’ll get 3x-18