In the book digital Signal Processing by Proakis 4th Edition, at page 593 a table is drawn about some second order modules for discrete time systems. In that table there Transposed Form II drawn But when I searched the net, it was drawn completely opposite to that drawn in the book. On the internet, the input and output were placed on right and left respectively. I want to ask that which form is correct?
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.