The Slitherlink solves to look like this:
You can ignore the red dots; I was just using those to confirm the solution. The answers to the clues are:
Weeds
- Drooping, withering: WILTING
- Uncomfortable, approaching cringeworthy: AWKWARD
- Sailing blue jellyfish: MAN-O-WAR
- Author of 700 Hobo Names: HODGMAN
- "Jumping Flea": UKULELE
- Periodical excerpted on Day 7: TV GUIDE
- Tapirs and zebras, but not giraffes: ODD-TOED
Flowers
- Chain of flowers: GARLAND
- Letter to embroider: INITIAL
- Tarot card with sphinxes: CHARIOT
- Preserved like a flower in a dictionary: PRESSED
- Flowers to make Dorothy sleep: POPPIES
- More verdant: GREENER
- Peter who assayed Poirot and Blackbeard: USTINOV
Then you fill the Slitherlink grid with these answers. I guess probably you make two copies of the Slitherlink grid and fill one with the Weeds answers and one with the Flowers answers. I tried to make images for this but they were impossible to read. TRUST ME. OR DO IT YOURSELF.
Anyway you want to focus on the cells that are marked with little flower dingbats. If you read off the marked letters outside the loop for the Flowers clues, it says NOPERS, because the flowers don't belong outside the loop. If you read off the marked letters inside the loop for the Weeds clues, it says WRONGO, because the weeds don't belong inside the loop.
The marked letters outside the loop for Weeds clues yield WALLED, and the marked letters inside the loop for Flowers clues spell GARDEN, and the answer is WALLED GARDEN.