This inequality is for one single unknown "k", so its solution is some set of real numbers in number line.


First, subtract 2k from both sides.  You will get an equivalent inequality

    2k - 2k - 6 > 3k - 2k + 2


Combine like terms.  You will get

    -6 > k + 2.


Next, subtract 2 from both sides.  You will get an equivalent inequality

    -6 - 2 > k + 2 - 2.


Combine like terms.  You will get

    -8 > k.


It is the same as

    k < -8.


At this point, the solution is completed.

The answer is  k < -8.


It is the set of all real numbers that are less than -8.


These numbers (the solution set) are located at the number line on the left from the point k= -8.

The point  k= -8  itself  IS NOT INCLUDED to the solution set.


Graphically, the solution set is shown below


       { k < -8 }
    ===================)------------------------------------

                      -8


Or, in the interval notation,  the solution set is  (-oo,-8).


The symbol  -oo  represents  "minus infinity".