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Outflowing gas from supermassive black holes in the centers of active galaxies has been postulated as a major contributor to galactic evolution. To explore the interaction between narrow-line region (NLR) outflows and their host galaxies, we use Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) spectra and Wide Field Camera 3 (WFC3) images of 15 nearby (z < 0.02) active galactic nuclei (AGN) to determine the extents and geometries of their NLRs. We combine new HST WFC3 continuum and [O III] $\lambda$5007A images of 11 AGN with 4 archival AGN to match existing spectra from HST STIS. For the 6 AGN with suitable long-slit coverage of their NLRs, we use isophotal fitting of ground-based images, continuum-subtracted [O III] images, and the STIS spectra, to resolve, measure, and de-project the gas kinematics to the plane of the host galaxy disk and distinguish NLR outflows from galaxy rotation and/or kinematically disturbed gas. We find an average [O III] extent of $\sim$680pc with a correlation between gas extent and [O III] luminosity of R$_\mathrm{[O III]}$ $\propto$ L$_{\text{[O III]}}^{0.39}$. The measured extents depend strongly on the depth of the [O III] images, highlighting the importance of adopting uniform thresholds when analyzing scaling relationships. The outflows reach from 39-88% of the full NLR extents, and we find that all 6 of the AGN with STIS coverage of their entire NLRs show strong kinematic evidence for outflows, despite previous uncertainty for these AGN. This suggests that NLR outflows are ubiquitous in moderate luminosity AGN and that standard criteria for kinematic modeling are essential for identifying outflows., Comment: Accepted for publication in ApJ on July 9, 2024. The paper has 21 pages, 10 figures, and 6 tables. Version two includes minor corrections to match the journal publication. The calibrated data are available through MAST at: https://archive.stsci.edu/hlsp/nlr-agn