Answer

Rust

use std::{collections::HashMap, hash::Hash};
fn group_by_most_common_element<T: Hash + Eq + Copy>(
    lists: Vec<Vec<T>>,
) -> HashMap<T, Vec<Vec<T>>> {
    // A global count of each element that i can refer back to
    let mut element_count = HashMap::new(); 
    // The final result map
    let mut result_map: HashMap<T, Vec<Vec<T>>> = HashMap::new(); 

    for list in &lists {
        for &element in list {
            // count each occurance of each element contained in list.
            *element_count.entry(element).or_insert(0) += 1;
        }
    }

    // represent all elements in the result map
    // even if they dont actually exist
    for &element in element_count.keys() {
        result_map.entry(element).or_default();
    }

    for list in lists {
        if let Some(most_common_element) = list
            .iter()
            // Find the most common element in the list based on the global count
            .max_by_key(|&element| element_count.get(element).unwrap_or(&0))
        {
            result_map
                // create a new element in the result map with the found most common element
                .entry(*most_common_element) 
                .or_default()
                // pushes the list to the array if it exists, or it creates one then pushes it on too.
                .push(list); 
        }
    }

    result_map
}
fn main() {
    let list: Vec<Vec<&str>> = vec![
        vec!["red", "green"],
        vec!["red", "blue"],
        vec!["red"],
        vec!["green", "blue"],
        vec!["blue", "yellow"],
        vec!["yellow"],
        vec!["yellow"],
        vec!["yellow", "red"],
        vec!["red"],
        vec!["green", "red"],
        vec!["red", "green"],
    ];
    let map = group_by_most_common_element(list);
    println!("{:?}", map);
}