under ' Body' in the homepage setting, I'm aware that we can choose three types of block which is text, item gallery and link. I have inserted several custom links, but I also wonder if we can put thumbnails of the custom link too? I'm using latest version of the homepage.
I've looked up to others' organization homepage and https://ijc.maps.arcgis.com/home/index.html here inserted custom links and thumbnails.
However, I realized they are using older version of AGOL homepage. So does this capabilities can only be done in older version of AGOL homepage?
Your existing home page looks like it is using custom HTML/CSS which was supported in the past, but for security reasons is no longer supported in the new home page editor.
However, you can great a gallery similar to what you have currently implemented using various groups of content, and the group graphic is what will appear in the gallery. That would, IMHO, be the easiest way to create something similar to what you have. Keep in my that groups can contain a variety of different contet, not just maps, apps, and layers, so you have complete flexibility in reproducing what you current have implemented.