To solve the equation \(-16.284(p - 14.27) = 56.994\), we start by dividing both sides by \(-16.284\):
\[ p - 14.27 = \frac{56.994}{-16.284} \]
Calculating the right-hand side:
\[ \frac{56.994}{-16.284} \approx -3.493169 \]
So we have:
\[ p - 14.27 \approx -3.493169 \]
Now, we add \(14.27\) to both sides to solve for \(p\):
\[ p \approx -3.493169 + 14.27 \]
Calculating the value of \(p\):
\[ p \approx 10.776831 \]
Rounding to the nearest tenth, we get:
\[ p \approx 10.8 \]
Thus, the answer is:
\[ \boxed{10.8} \]