Answer: $24$

Explanation:1. Expand the expression $(x+3)^{2}$: $(x+3)^{2} = (x+3)(x+3)$ Using the FOIL method (First, Outer, Inner, Last): $x \cdot x + x \cdot 3 + 3 \cdot x + 3 \cdot 3$ $= x^{2} + 3x + 3x + 9$ $= x^{2} + 6x + 9$

2. Substitute this expanded form back into the given equation: The given equation is $(x+3)^{2}=33$. Substituting the expanded form, we get: $x^{2} + 6x + 9 = 33$

3. Isolate the expression $x^{2}+6x$: We want to find the value of $x^{2}+6x$. From the equation $x^{2} + 6x + 9 = 33$, subtract 9 from both sides: $x^{2} + 6x = 33 - 9$ $x^{2} + 6x = 24$

4. Conclusion: The value of $x^{2}+6x$ is $24$.