Let's solve the equation step by step.
Starting with the equation:
\[ 4(3x + 2) + 3 = 35 \]
Step 1: Distribute the 4:
\[ 12x + 8 + 3 = 35 \]
Step 2: Combine like terms:
\[ 12x + 11 = 35 \]
Step 3: Subtract 11 from both sides:
\[ 12x = 35 - 11 \]
\[ 12x = 24 \]
Step 4: Divide by 12:
\[ x = \frac{24}{12} \]
\[ x = 2 \]
Thus, the value of \( x \) is \( \boxed{2} \).