JSFiddle - React, Tailwind, and code Playground

JavaScript

function LetterCountI(str) {
    var result = -1,
        largestCount = 1;
    var words = str.split(" ");

    for (var i = 0; i < words.length; i++) {
        var word = words[i];
        var repeat = GetWordRepeatCount(word);
        if (repeat > largestCount) {
            largestCount = repeat;
            result = word;
        }
    }

    return result;
}

function GetWordRepeatCount(str) {
    //get each letter count for the word
    var counts = {};

    for (var i = 0; i < str.length; i++) {
        var char = str[i];
        counts[char] = (counts[char] || 0) + 1;
    }

    //get the largest number for the letter counts
    var max = 0;

    for (var c in counts) {
        if (counts[c] > max) max = counts[c];
    }

    return max;
}

console.log(LetterCountI("Hello there"));
console.log(LetterCountI("No words"));
console.log(LetterCountI("How about these words?"));