use pythagorus, a² + b² = c²
in this case you have c and either a or b. (it doesn't matter which, i'll use a)
using a bit of algebra, you can turn your formula into b = [tex] \sqrt{(c² - a²)} [/tex]
now all you have to do is plug in your numbers. a = 6mm and c = 9mm
b = [tex] \sqrt{((9)² - (6)²)} [/tex] = [tex] \sqrt{(81 - 36)} [/tex] = [tex] \sqrt{45} [/tex] ≈ 6.7mm