lim 6(x + Δx) − 6x / Δx Δx→0 I dont get it, why is it = 6. I found the nominator after distributed = 6Δx/ Δx. Let Δx= 0 and 0/0 = 0?

"why is it = 6"
You answered your own question.

"6Δx/ Δx"
and for any value of Δx which is not 0, those cancel out leaving you with 6.

"Let Δx= 0"
No, don't do that. That's not what "limit as Δx APPROACHES 0" means. It means as you take a sequence of values of Δx that ARE NOT 0 but ARE GETTING CLOSER AND CLOSER TO 0, what is the trend? That's why the phrase uses the word "APPROACHES".

If you take any such sequence of nonzero values getting closer and closer BUT NOT EQUALLING 0, you will get 6 for every one. And so the trend of the sequence of values 6, 6, 6, 6, 6, .... is 6.

Lim (6(x + Δx) − 6x) / Δx Δx→0
= Lim (6x + 6Δx − 6x) / Δx Δx→0
= Lim (6 Δx) / Δx Δx→0
= 6 ................... dividing out Δx from the numerator and denominator