First, multiply the quotient and the divisor. Then, add 19 to the answer. That will be your equation (answer) to the problem.
( 3x^2 + 2x + 4 ) ( 2x -3 )
= 6x^3 + 4x^2 + 9x^2 + 8x - 6x - 12
= 6x^3 + 13x^2 + 2x - 12 + 19 *+19 is the remainder.
= 6x^3 + 13x^2 + 2x + 7 (Final Answer)
Then check your answer by dividing 6x^3 + 13x^2 + 2x + 7 by 2x - 3