Question

4(x + 3) + 2x = 6(x + 2)

5 + 2(3 + 2x) = x + 3(x + 1)

5(x + 3) + x = 4(x + 3) + 3

4 + 6(2 + x) = 2(3x + 8)

which one has no solutions ?

Answer 1

The second option is your answer. 

5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3x + 3
11 + 4x = 4x + 3

Subtract 4 from both sides. You are left with an untrue statement:
11 = 3
11 ≠ 3 so therefore your answer is no solution. 

Answer 2

Let’s try to look at each one.

First one:
4(x+3)+2x=6(x+2)
We can multiply.
4x+12+2x=6x+12
By looking at this, you can tell it’s equal due to the fact when you add like terms, they will have to same answer.

Second one:
5+2(3+2x)=x+3(x+1)
Let’s multiply.
5+6+4x=x+3x+1
I can already tell this isn’t equal. One has +11 and the other has +1. To make sure, let’s have x=1
5+2(3+2)=1+3(1+1)
5+2(5)=1+3(2)
5+10=1+6
15=7
7 and 15 are not the same number, so the second one doesn’t have any solutions.