Final answer:
Danica can arrange the flowers into 6 vases.
Step-by-step explanation:
To find the greatest number of vases that Danica can arrange, we need to find the greatest common divisor (GCD) of the number of roses and tulips. In this case, the GCD of 36 and 42 is 6. Therefore, Danica can arrange the flowers into 6 vases.