Is it possible to draw a tringle with 90 angle and one leg that is 8 centimeters long and one leg that is 6 centimeters long? is there more than one such tringle that exists with these conditions?

Yes it is The hypotenuse  is  10 cms long.
Because its a right angled triangle ( 90 angle)  the hypotenuse will be 10 cms long - it will obey the Pythagoras theorem:-

10^2 = 8^2 + 6^2

There is only one  right angled triangle with these measurements but there are many  of them which have sides in same ratio

for example 

3, 4 and 5

9,12 and 15

12, 16 and 20  and so on..