How can I rid my garden of houtonyia ?

I couldn't find anything specific for houtonyia. My good friend google thought it was a slug, Japanese beetle or an small animal.. Oh google, you failed me today.

When I changed the search terms to invasive plants, it worked much better. Here's one of many articles to read.

https://www.thespruce.com/best-way-to-get-rid-of-invasive-plants-2132644

You don't say if these are mixed in your garden or pretty much buy themselves. I made the mistake of planting Woodruff in a skinny garden space between my patio and garage. After a few years it just took over and I couldn't plant any colorful flowers there. I finally decided to get rid of them. Here's how. In the fall when everything is done, I used my favorite weed killer (you can use natural homemade or commercial) on the entire patch. Then I covered it with black plastic and weighed it down with some dirt. The following summer I only used potted plants there. The summer after that I removed the dirt, and plastic then put in new dirt and planted flowers. The Woodruff was 99.9% gone from that area. I did find one tiny piece at the end of the garden but immediately pulled it out and had to do that for that whole summer but in the fall I sprayed it nd it never came back.

HTH