Answer
No.
Work Step by Step
To test if $x=\frac{1}{3}$ is a zero, evaluate $f(\frac{1}{3})=2(\frac{1}{3})^3+3(\frac{1}{3})^2-6(\frac{1}{3})+7\approx5.4$ and this is the remainder. As the remainder is not zero, $x=\frac{1}{3}$ is not a zero of the function.
