Rate of change of the hypotenuse

Since the triangle is right-angled with legs $8$ and $x$, the hypotenuse satisfies $h^2 = 8^2 + x^2$. Differentiating both sides with respect to $t$ gives $2h\frac{dh}{dt} = 2x\frac{dx}{dt}$, so $\frac{dh}{dt} = \frac{x}{h}\frac{dx}{dt}$.

At the instant in question, $x = 6$, so $h = \sqrt{8^2 + 6^2} = \sqrt{100} = 10$. Substituting $x = 6$, $h = 10$, and $\frac{dx}{dt} = 3$ gives $\frac{dh}{dt} = \frac{6}{10}(3) = 1.8$ units/s.