Identify the conditions for the function to be defined in real numbers.

The given function is $f(x) = \sqrt{\frac{2}{x-2}} - 3$.
For $f(x)$ to be a real number, two conditions must be met:

1. The expression under the square root must be non-negative: $\frac{2}{x-2} \ge 0$.
2. The denominator of the fraction cannot be zero: $x-2 \ne 0$.

From $x-2 \ne 0$, we know that $x \ne 2$.

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