Verified answer

[tex]\displaystyle\bf\\\frac{x}{y} =\frac{1}{2} \ \ \ \Rightarrow \ \ \ y=2x\\\\\\\frac{4x^{2} -9y^{2} +2xy}{3y^{2} +16x^{2} }=\frac{4x^{2} -9\cdot(2x)^{2}+2x\cdot 2x }{3\cdot(2x)^{2} +16x^{2} } =\frac{4x^{2} -36x^{2} +4x^{2} }{12x^{2} +16x^{2} } =\\\\\\=\frac{-28x^{2} }{28x^{2} } =-1[/tex]