First you have to find the greatest common factor between the two terms. You can first start by finding all the factors of 18 and 32: 18 --> 1,2,3,6,9,18 32 --> 1,2,4,8,16,32 (Here we kept 32 positive so it is easier to find the factors and you don't get confused by the subtraction symbol)
Out of all these factors, the only ones 18 and 32 have in common is 2. Now that you know the GCF (greatest common factor), you can now divide both terms by 2: 18k/2 = 9k 32k/2 = 16k
Since the constant/number 2 does not have a variable, it does not affect the variables in the other two terms only the constants. Now you can put 9k and 16k where 18k and 32k: 9k-16k
You cant just leave 9k-16k by itself because all you are doing is putting the expression into simpler terms, not taking away parts of it. This is where the 2 you divided from both sides comes into play.
The only thing left to do is put parentheses around 9k-16k and put the 2 on the outside. Now your polynomial is factored: 2(9k-16k)
