This is the 13411th most frequent Russian word.
наибольшие
"Наибольшие" means "the greatest" or "the largest."
The word 'наибольшие' is used as a superlative adjective, modifying 'шансы' (chances), indicating that his chances are the greatest among all possibilities.
У него наибольшие шансы на успех.
He has the greatest chances for success.
Here, 'наибольшие' is used as a superlative adjective describing 'трудности' (difficulties), denoting that these difficulties are the most significant ones compared to others in the given context.
Наибольшие трудности возникли на начальном этапе проекта.
The greatest difficulties arose at the initial stage of the project.
In this example, 'наибольшие' serves as a superlative adjective qualifying 'успехи' (successes), specifying that the student's achievements surpass others in the specified field.