data – Pattern Matching in 2-dimensional lists

How would I search for all the elements in a nested list which contain values at specific index? For example, I want to search for and return all the elements in a (n,2) list which begin with a 3 ({3, …}).

How would I generalize it to return all elements of a list which begin with a 3 of any length, or of a fixed length if the inner lists are of variable length?