When the school was going to lead a trip to Oaxaca, the principal suggested that the Spanish teacher go, since she speaks the language fluently.
When the school was going to lead a trip to Oaxaca, the principal suggested that the Spanish teacher would go, since she speaks the language fluently.
When the school was going to lead a trip to Oaxaca, the principal suggested that the Spanish teacher go, since she speaks the language fluently.
When the school was going to lead a trip to Oaxaca, the principal suggested that the Spanish teacher would go, since she speaks the language fluently.
The verb "suggest" idiomatically takes a "that"-clause. A suggestion of a course of action should be phrased in the subjunctive mood.