This version of the Hotchkiss 6-pounder is fitted with a recoil brake, noticeable underneath the gun tube. It is also fitted with two side plates. These support parts of the recoil mechanism, but it is difficult to guess how they work, exactly, from most photos.
In 2017 I found some fairly good 3-view drawings of the recoil mechanism for a Hotchkiss 3-pounder. Here is a side view:
The basic components include the brake cylinder, a U-shaped cradle with a front bridge arcing beneath the barrel, and the gun tube suspended on slides within the cradle. The slide and guide rails are more evident in a view from behind:
The 3-pdr drawings show what elements to look for but do not directly apply to the 6-pounder.
Finally I came across a photo snapped of a 6-pdr on the USS Olympia that is a great help. It was taken from behind and the traversing arm has been removed, so there is an unobstructed view.
The photo clearly shows the thickness of the plate, and since it has not been painted over, it is possible to see the merest outline of the slide it contains and guides. Here is a CAD sketch of the two plates with the slides extended to the rear, as they would be in operation.
The CAD image and file are labelled "Guides & Slides." Note that the slides are beveled top and bottom to lock them into the guides. The gun tube is attached to the slides, and the guide plates carry "new" outboard trunnions. These replace the trunnion that was solidly molded into the barrel in the earlier Hotchkiss 6-pounders, which had no recoil brake save the crinoline mount.
Not shown is a front bridge that arcs under the barrel and connects the two side plates to form a typical U-shaped gun cradle.