To solve the equation given:
\[ 16 + -3(f + 4) = 9f - 8 \]
We can start by distributing \(-3\) in the term \(-3(f + 4)\):
\[ -3(f + 4) = -3f - 12 \]
Now the equation becomes:
\[ 16 - 3f - 12 = 9f - 8 \]
Next, simplify the left side:
\[ 16 - 12 = 4 \]
So now we have:
\[ 4 - 3f = 9f - 8 \]
Next, let's get all terms involving \(f\) on one side and the constant terms on the other side. We can add \(3f\) to both sides:
\[ 4 = 12f - 8 \]
Now add \(8\) to both sides to isolate the \(f\) term:
\[ 4 + 8 = 12f \] \[ 12 = 12f \]
Now divide both sides by \(12\):
\[ f = 1 \]
Thus, the solution to the equation is \(f = 1\).
If you want to find the expression \(16 + ?\), it seems like you are asking for what would be added to \(16\) so that the entire equation holds true. However, it is not clear from your question what the exact parameter was for placing \(+\) or what should replace the question mark.
If you're looking for the steps to derive the original equation or to confirm the value of \(f\) for getting back to an original equation, please provide more context or clarify your question so I can assist you better!