Answer
In applying the FOIL method, the inner product was missed.
$3x^2-2x-8$
Work Step by Step
$(x-2)(3x+4)\longrightarrow$ use the FOIL method to multiply the binomials
$x(3x)+x(4)-2(3x)-2(4)\longrightarrow$ multiply
$3x^2+4x-6x-8\longrightarrow$ combine like terms
$3x^2-2x-8$