Answer: [tex]\boldsymbol{2(x-2)(5x+7)}[/tex]
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Work Shown:
[tex](4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\[/tex]
The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.
The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.
Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.
Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.