Please confirm.
These rules are not int practice. Is this true?
Because 30 years ago in high school, I was taught.
x/zero is infinity, error in computer.
zero/zero is undefined, not zero. Also error in computer.

So zero/zero is undefined or zero?
Thanks for anyhelp confirming my doubt.
[Add: is not in practice today, implying that in the old days some calculation still use zero/zero = zero.
When was it's not in practice?]

No.
The limit doesn't exist. If you don't understand why, read up on left-hand and right-hand limits.

Correct

Correct, although it would normally be written as ##\lim_{h \to 0} \frac{6h}{3h} = 0##. In other words, without the last arrow, which indicates "approaches."

Edit: I miswrote 0 instead of 2 as the limit. It should be ##\lim_{h \to 0} \frac{6h}{3h} = 2##

You mean ##\lim_{h \to 0} \frac{6h}{3h} = 2##?
The "last arrow" I think is ambiguous in math.
I should have said ##\lim_{h \to 0} \frac{6h}{3h}## is equal/match to 2.

I want to be a bit more careful than what Mark says. Although in principle I agree with him, you seem to use arrows ##\rightarrow## everywhere, and it is not clear to me why you write this arrow. So the following are correct:

A. ##\lim_{h\rightarrow 0} \frac{6}{h}## is undefined.
B. If ##h=0##, then ##\frac{6}{h}## is undefined.
C. ##\lim_{h\rightarrow 0}\frac{6h}{h} = 6##.
D. If ##h=0##, then ##\frac{6h}{h}## is undefined.

I should have asked directly to Mark44, but your post is the last one.

Actually this

doesn't have anything to do with "left-hand and right-hand limits", because it's the last arrow that I put wrongly? I just read left-hand, right-hand arrow, http://www.millersville.edu/~bikenaga/calculus/limlr/limlr.html [Broken]
but it doesn't explain why there's no limit.

The point of the left-hand and right-hand limits is the following:
While
[tex]\lim_{h\rightarrow 0} \frac{6}{h}[/tex]
is undefined. It is true that the left-hand limit
[tex]\lim_{h\rightarrow 0-} \frac{6}{h} = -\infty[/tex]
and the right-hand limit is
[tex]\lim_{h\rightarrow 0+}\frac{6}{h} = +\infty[/tex]

Ahh, so if the left hand and the right hand lmits differs very big, than we can say "There is no limit"?
[Add: differ is the wrong word I think. So, the left-hand and the right-hand limit must match/exact?]
[Add: ##\lim_{h \to 0+} \frac{6h}{h}## is equal to ##\lim_{h \to 0-} \frac{6h}{h}##, so we can say that there is a "limit" there?]

Part of the problem is that you are trying to interpret "infinity" as if it were a number- it isn't. Saying that a limit "is equal to infinity" is the the same as saying the limit "does not exist", just in a particular way.