I will take it from there.

$$4(x+2)=5x$$

Now, substitute the $$x$$, but I will start with 8.

$$4(x+2)=5x\Rightarrow4(8+2)=5(8)\Rightarrow4(10)=40\Rightarrow40=40\\\\\mbox{We\;can\;now\;see\;that\;the\;equation\;is\;true,\;so\;}x=40.$$

Let's substitute x into 8

x=8

now change everything into fractions

now, I don't get it. It has to be 2 4/8, bit 4/8. Can someone please help?

5:x+2=4:x

I think that the question is supposed to be

5:(x+2)=4:x

$$\\\frac{5}{x+2}=\frac{4}{x} \\\\
\frac{x+2}{5}=\frac{x}{4}\qquad \mbox{I turned both sides upside down}\\\\
\frac{20(x+2)}{5}=\frac{20x}{4}\qquad \mbox{I multiplied both sides by 20}\\\\
4(x+2)=5x\qquad \mbox{}\\\\$$

You should be able to do it from here.

You have used a trial and error method to solve this.   (Even though you only had one trial)  Your answer is correct.

Try  watching how other questions like this are solved and you will learn the high school method. 

Some questions are just too difficult to use trial and error  

Ok. I kind of don't get what you said in the trial thing.

You "trialled"  x=8 and it worked.

You did not show us that you had "trialled" any other number .  

Oh. I now get it. Even on the first post, I wrote out 8! Interesting...