Let the mean of the last four observations be $A_2$. Then, by the formula for combined mean, we get,

$15=\frac{6\times 16+4\times A_2}{6+4}$ 

or $150=96+4A_2$ 

$\therefore A_2=\frac{54}{4}$

Let the sixth number is $x$, then taking the sixth number as a collection, the combined mean of this collection and the collection of the last four is $12$.

$\therefore$ By the definition of combined mean

$12=\frac{1\times x+4\times \frac{54}{4}}{1+4}$

$$\begin{gathered} \therefore 60=x+54 \\ \therefore x=6 \end{gathered}$$

Hence, the sixth number $=6$