\(\displaystyle \lim_{x\to 4} \frac{2x^3\,-\,128}{sqrt {x}-2} \, \times \,\frac{sqrt {x}\,+\,2}{sqrt {x}\,+\,2}\)

\(\displaystyle \lim_{x\to 4} \frac{2(x^3\,-\,64)(\sqrt{x}\,+\,2)}{x\,-\,4}\)

\(\displaystyle \lim_{x\to 4} \frac{2(x\,-\,4)(x^2\,+4x\,+16)(\sqrt{x}\,+\,2)}{x\,-\,4}\)

\(\displaystyle \lim_{x\to 4} 2(x^2\,+4x\,+16)(\sqrt{x}\,+\,2)}= 2(16\,+\,16\,+16)(2\,+\,2)=48 \, \times\, 8=384\)