Answer
This expression represents the slope of the tangent of the function $f(x)=x^4$ at $a=2$ and its value is $m_{tan}=32.$
Work Step by Step
The definition of the slope of the tangent at $a$ is given by
$$m_{tan}=\lim_{h\to0}\frac{f(a+h)-f(a)}{h}.$$
We see that if we take $f(x)=x^4$ and $a=2$ (and also we calculate $f(a)=f(2)=2^4=16$) the upper expression becomes the expression for the slope of $f(x)=x^4$ at $a=2$. Let us calculate this slope. We will use that $c^4-d^4=(c^2+d^2)(c^2-d^2)=(c^2+d^2)(c+d)(c-d):$
$$m_{tan}=\lim_{h\to0}\frac{(2+h)^4-16}{h}=\lim_{h\to0}\frac{(2+h)^4-2^4}{h}=\lim_{h\to0}\frac{((2+h)^2+2^2)(2+h+2)(2+h-2)}{h}=\lim_{h\to0}\frac{((2+h)^2+4)(4+h)h}{h}=\lim_{h\to0}((2+h)^2+4)(4+h)=((2+0)^2+4)(4+0)=32.$$
