To determine how many solutions the equation \( 16q + 18 - 6 = 13q - 18 \) has, we'll first simplify and solve the equation.
Starting with the given equation:
\[ 16q + 18 - 6 = 13q - 18 \]
We can simplify the left side:
\[ 16q + 12 = 13q - 18 \]
Next, we will isolate \( q \) by first getting all terms involving \( q \) on one side and constant terms on the other side:
Subtract \( 13q \) from both sides:
\[ 16q - 13q + 12 = -18 \]
This simplifies to:
\[ 3q + 12 = -18 \]
Now, subtract 12 from both sides:
\[ 3q = -18 - 12 \]
This simplifies to:
\[ 3q = -30 \]
Next, divide both sides by 3:
\[ q = -10 \]
Since we found one unique solution \( q = -10 \), we conclude that the equation has exactly one solution.