The value of k that makes the inequality have no solution is -2 .
Explanation
Given inequality is....
[tex]2kx - 3k < 2x + 4 + 3kx[/tex]
First we will get only the x-terms together in left side. So....
[tex]2kx-2x-3kx<3k+4\\ \\ -kx-2x<3k+4\\ \\ x(-k-2)<3k+4[/tex]
Now for getting no solution, the co efficient of 'x' should be 0. That means...
[tex]-k-2 =0\\ \\ k= -2[/tex]
So, the value of 'k' for getting no solution will be -2.
