To solve the equation \( 2x^{1/3} + 6 = 18 \), we can start by isolating the term involving \( x \).
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Subtract 6 from both sides: \[ 2x^{1/3} = 18 - 6 \] \[ 2x^{1/3} = 12 \]
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Divide both sides by 2: \[ x^{1/3} = \frac{12}{2} \] \[ x^{1/3} = 6 \]
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To eliminate the cube root, cube both sides: \[ (x^{1/3})^3 = 6^3 \] \[ x = 216 \]
Thus, the solution for \( x \) is: \[ \boxed{216} \]