The simplest and most straightforward way is to write the system of equations assuming that 

"the maximum capacity available is utilized" and then to check if it has solution/solutions in integer non-negative numbers.


This system of equations is


4*A + 1*B = 195  hours   (1)   ("The maximum capacity for assembly  is 195 hours")
3*A + 2*B = 165  hours   (2)   ("The maximum capacity for finishing is 165 hours")


Apply the Substitution or Elimination method - on your choice - to get the solution


A = 45,  B = 15.


Since the system has (admits) the solution in integer numbers, it is the 


Answer.  A = 45 and B = 15.