To solve the equation \(3(2y+6)=42\), we can start by distributing the 3 on the left side:
\[ 3 \cdot 2y + 3 \cdot 6 = 42 \]
This simplifies to:
\[ 6y + 18 = 42 \]
Next, we want to isolate the term with \(y\). We can do this by subtracting 18 from both sides of the equation:
\[ 6y + 18 - 18 = 42 - 18 \]
This simplifies to:
\[ 6y = 24 \]
Now, to solve for \(y\), we divide both sides by 6:
\[ y = \frac{24}{6} \]
This gives us:
\[ y = 4 \]
So the solution is:
\[ \boxed{4} \]