The model and serial #'s have been removed from my brother's mower. Also looks like there was a transmission control on the deck that has been removed and a variable speed transmission installed. I am new to the Honda mower world and just don't know enough to identify this machine, I am pretty sure it is the GVX160 motor
Looks like an HRC216HXA (K0 or K1 model/version), and the labels indicate it is a hydrostatic, variable speed transmission (shaft drive). These do come with the GXV160 (160cc pushrod-type overhead valve commercial-grade) engine.
The opening in the left rear of the mower deck is for a shift lever for the gear-transmission model (HRC216SX). Both the gear and hydrostatic models use the same deck. This is either the first (K0) or second (K1) version of this model. Newer ones (K2, K3) use a different deck, and are hydrostatic only, and don't have that opening.