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The solutions to 2x^2 - 10x + 5 = 0 are (5 +/- sqrt(15))/2  Plugging these values in, you get

(2*(5 + sqrt(15))/2 - 3)(4*(5 - sqrt(15))/2 - 6) = -18

(2a - 3) ( 4b - 6)  =

(2a - 3) (2) (2b - 3)  =

2 ( 2a - 3) (2b - 3)  =

2 [ 4ab - 6a - 6b + 9 ]

2 [ 4ab  - 6 ( a+ b) + 9 ] 

The product of the roots = 5/2

The sum of the roots = - (-10) / 2 =  5

So

2 [  4 (5/2)  - 6 ( 5)  + 9 ]  =

2 [ 10 - 30 + 9 ]  =

2 [ -11 ]  = 

-22

Another solution! :D

P(x) = 2x^2 - 10x + 5 = 2(x - a)(x - b)

(2a - 3)(4b - 6) = 8(a - 3/2)(b - 3/2)

P(3/2) = 2(3/2 - a)(3/2 - b) = -11/2

-11/2 * 4 = -22.