I fell that I don’t have enough information to adequately translate this sentence because it is a kind of “out of context”. Nevertheless, it seems that they are talking about a hypothesis test to be applied to a given hypothesis (the secondary global hypothesis) that has two possible outcomes (the two comparisons within it).
Spanish speaking statisticians, refers to two-sided tests as “tests a dos colas”. I believe that with Hochberg approach they refer to the Benjamini-Hochberg test or to a similar one. These tests are used to correct for false discovery rates, which represent a problem when large numbers of experiments are performed (hundreds or thousands).

Thus, a nice translation for the whole phrase could be: El Error de Tipo I para la hipótesis global secundaria se controlará, para las dos comparaciones posibles correspondientes, mediante un test a dos colas y aplicando el método de Hochberg.