To solve for \( x \) in the equation
\[ x^{16} = 16^{12}, \]
we can start by rewriting \( 16 \) as a power of \( 2 \):
\[ 16 = 2^4. \]
Substituting this into the equation gives:
\[ x^{16} = (2^4)^{12}. \]
Using the property of exponents \( (a^m)^n = a^{mn} \), we have:
\[ (2^4)^{12} = 2^{4 \cdot 12} = 2^{48}. \]
So now we can rewrite the equation as:
\[ x^{16} = 2^{48}. \]
Next, we can express \( x \) as a power of \( 2 \):
\[ x = 2^k \quad \text{for some } k. \]
Now substituting \( x \) into the equation gives:
\[ (2^k)^{16} = 2^{48}. \]
Using the property of exponents again:
\[ 2^{16k} = 2^{48}. \]
Since the bases are the same, we can set the exponents equal to each other:
\[ 16k = 48. \]
To solve for \( k \), divide both sides by \( 16 \):
\[ k = \frac{48}{16} = 3. \]
Thus,
\[ x = 2^k = 2^3 = 8. \]
The solution is
\[ \boxed{8}. \]