How is p(y* |x) computed for error analysis

In deciding which part of the model to target p(y*|x) and p(y^ |x) is first computed.

Where have you seen this notation?

for computing the error analysis, course 5 week 3

First you look up P(y^{*<1>} \mid x) after you have fed x through the encoder block, then you feed x and y^{*<1>} to find P(y^{*<2>} \mid x, y^{*<1>}) etc. Multiply everything to get the total probability.