The best way to get high engagement on a Facebook page is simply to publish multiple photos / images in a single post, with an enticing caption, ideally ending with a CTA (call to action) to reap the benefits of engagement.
Each view on one of the images will increment Facebook's engagement counter, which will contribute to your post's (and page's) authority. A virtuous circle.
Post at least 5 images together to get a good result. Obviously great looking inspiring images work best.
I've written a longer post re: ways to increase Facebook engagement on my other blog, right here. Spoiler: job postings & 360° photos/videos.