To find the number of solutions to the equation \( 16q + 18 - 6 = 13q - 18 \), we start by simplifying the left side:
\[ 16q + 18 - 6 = 16q + 12 \]
Now, we can rewrite the entire equation:
\[ 16q + 12 = 13q - 18 \]
Next, we will isolate the variable \( q \) by moving all terms involving \( q \) to one side and constant terms to the other side. We can subtract \( 13q \) from both sides:
\[ 16q - 13q + 12 = -18 \]
This simplifies to:
\[ 3q + 12 = -18 \]
Now, we will subtract 12 from both sides:
\[ 3q = -18 - 12 \] \[ 3q = -30 \]
Next, we divide both sides by 3 to solve for \( q \):
\[ q = -10 \]
Since we found a single value for \( q \), the equation has one solution.
In conclusion, the original equation \( 16q + 18 - 6 = 13q - 18 \) has only one solution: \( q = -10 \).