<em>¿cuántos tienes?</em><em> </em>translates into <em>how many do you have? </em>because they are talking about countable things and we know this because of the reply of Rosa that says I have four (tengo cuatro). So cuántos for a number of things. On the other hand, tengo comes from the verb tener and is its conjugation for the first person singular in the simple present.