Answer
$5\times10^{-3} \ kg$
Work Step by Step
We simplify the equation for the period to obtain:
$$T = \frac{2\pi}{\sqrt{\frac{(m+M)gl}{I}}}\\ T = \frac{2\pi}{\sqrt{\frac{(m+M)g\frac{mr}{m+M}}{(m+M)r^2}}}\\ T = \frac{2\pi}{\sqrt{\frac{gm}{(m+M)r}}}\\ 12 = \frac{2\pi}{\sqrt{\frac{(9.81)m}{(m+.6)(.3)}}} \\ m = 5\times10^{-3} \ kg$$
