How do you subtract an integer from another integer without using a number line or counters

I'm assuming you mean negative integers and mixed. -3--3=? When to negatives are back to back it turns in to a positive number. The equation becomes -3+3=0.

Adding 2 negative numbers will always result in a negative value. -3+-3=-6.

A negative times a negative is always a positive . -2x-2=4

A positive integer times a negative integer will be a negative value. -3x4=-12.

A negative divided by a negative is a negative. -12/-2=-6

A positive divided by a negative is a negative. 9/-3=-3