Answer:
One
Step-by-step explanation:
   Since we have a 90° angle and a 20° angle, the last angle must be 70°.
180° - 90° - 20° = 70°
   Now we also have the requirement of a 6-unit side between the 90° and 20° angles.
   With all of these requirements, we can only draw one triangle like this since we have an angle, an angle, a required third angle, and a side.