To find out how much of the craft project Katie completes in one hour, we first determine her rate of completion based on the information provided.
Katie completes \(\frac{2}{3}\) of the project in \(\frac{3}{4}\) of an hour. We can express her completion rate as follows:
\[ \text{Rate} = \frac{\text{Work completed}}{\text{Time taken}} = \frac{\frac{2}{3}}{\frac{3}{4}} \]
To divide the fraction \(\frac{2}{3}\) by \(\frac{3}{4}\), we multiply \(\frac{2}{3}\) by the reciprocal of \(\frac{3}{4}\):
\[ \text{Rate} = \frac{2}{3} \times \frac{4}{3} = \frac{2 \times 4}{3 \times 3} = \frac{8}{9} \]
This means Katie completes \(\frac{8}{9}\) of the project in one hour since we calculated her rate per hour.
Thus, the fraction of the craft project that Katie completes in one hour is
\[ \boxed{\frac{8}{9}}. \]
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