Step 1 :Between the numbers 6 and 7, there are no integers, as integers are whole numbers and there are no whole numbers between 6 and 7.
Step 2 :However, there are infinitely many real numbers between 6 and 7, as real numbers include both rational and irrational numbers.
Step 3 :\(\boxed{\text{Final Answer: Between the numbers 6 and 7, there are infinitely many real numbers.}}\)