Hello an,
Rather than work these specific problems, let's use general functions to develop theorems which we can then use to answer the questions.
i) Linear functions.
Let $$f(x)=ax+b$$
and so the difference quotient is:
$$\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to0}\frac{(a(x+h)+b)-(ax+b)}{h}=\lim_{h\to0}\frac{ax+ah+b-ax-b}{h}=\lim_{h\to0}\frac{ah}{h}=\lim_{h\to0}a=a$$
ii) Quadratic functions.
Let $$f(x)=ax^2+bc+c$$
and so the difference quotient is:
$$\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to0}\frac{\left(a(x+h)^2+b(x+h)+c \right)-\left(ax^2+bx+c \right)}{h}=$$
$$\lim_{h\to0}\frac{ax^2+2ahx+ah^2+bx+bh+c-ax^2-bx-c}{h}=\lim_{h\to0}\frac{2ahx+ah^2+bh}{h}= \lim_{h\to0}(2ax+ah+b)=2ax+b$$
Now we may answer the questions:
1.) This is a linear function. We identity $a=2,\,b=-3$ and so:
$$\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=a=2$$
2.) This is a quadratic function. We identity $a=2,\,b=-3,\,c=0$ and so:
$$\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=2ax+b=4x-3$$