1.
Try to factor the number 192 into the product of two positive integers with the difference of 4 between them.

Actually, such factorization is unique: 192 = 16*12.

So, the number of columns is 12.


2.
The other way is to solve the problem using equations.

Let x be the (unknown) number of columns.
Then the number of rows is x+4, and your equation is 

x*(x+4) = 192,  or   = .

Now you can apply the quadratic formula or use factoring. Let's factor left side polynomial: 

 = (x+16)*(x-12).

Then your equation is (x+16)*(x-12) = 0.

Its roots are x = -16 and x = 12.

Only positive x = 12 suits the condition.

Answer. 12 columns.