If one-third of one-fourth of a number is $15$, then three-tenth of that number is:

Let the unknown number be $x$.
According to the problem statement:

$$\frac{1}{3}\times \frac{1}{4}\times x=15$$

$$\frac{1}{12}x=15$$

$$x=15\times 12=180$$

Now, we find three-tenth of this number:

$$\text{Required Value}=\frac{3}{10}\times 180=3\times 18=54$$