To determine the missing value that would make the equation \(3 (5x + 6) = 3x + [?]x + 18\) have zero solutions, we first simplify both sides of the equation.
Starting with the left side:
\[ 3(5x + 6) = 15x + 18 \]
Now, let's rewrite the right side with the missing value represented as \(a\):
\[ 3x + ax + 18 \]
This can be combined to:
\[ (3 + a)x + 18 \]
Now, we set the two sides of the equation equal to each other:
\[ 15x + 18 = (3 + a)x + 18 \]
Next, we'll subtract \(18\) from both sides:
\[ 15x = (3 + a)x \]
To have zero solutions, the left side cannot equal the right side for any \(x\), which means the coefficients of \(x\) on both sides must be equal (and thus give us a contradiction). This leads us to set:
\[ 15 = 3 + a \]
Now, we solve for \(a\):
\[ a = 15 - 3 = 12 \]
Thus, the value of \([?]\) that would make the equation \(3 (5x + 6) = 3x + [?]x + 18\) have zero solutions is:
\[ \boxed{12} \]