The Council fathers decided not to use the type of solemn definition found in many, not all, past Ecumenical Councils. So without a solemn definition, how can the teachings be infallible? There are three types of infallible teachings of the Magisterium:
1. solemn definitions of the Pope
2. solemn definitions of a Council
3. the ordinary universal Magisterium, when the Pope and the body of Bishops are in agreement on one position definitively to be held
Though #3 is usually conceived as occurring when the Bishops are dispersed in the world, they do not lose that ability when gathered in a Council. So when a Council like Vatican II uses #3, they teach infallibly without a solemn definition. And this explains how a Council can be infallible in all that it teaches, whether a solemn definition is used or not.