Transposed Direct Form II
Direct-Form II is the canonical structure to implement an LCCDE, using minimum number of delay elements and multiplications. The input $x[n]$ is placed on the left, and the output $y[n]$ is on the right, complying with the signal processing conventions.
DF-II structure, implements the poles (IIR part) before the zeros (FIR part), however this may be undesirable for numerical issues with high gain poles.
The transposed DF-II structure, which maintains the canonical advantage of DF-II while avoiding the potential numerical instability of it, is obtained by reversing all branch directions, and replacing sum nodes with signal nodes, also replacing (and renaming) the input output nodes too; hence input becomes at the right side and output emerges at the left node. Transposed DF-II implements zeros first, and poles later.
However, for convenience, to comply with the convention that the input is applied at the left node, the transposed DF-II structure is horizontally flipped. This way, input $x[n]$ appears at the left again.
Both forms of transposed DF-II are equivalent.