var datas = ["11/04/2021", "11/03/2021", "08/12/2021", "20/04/2021"];
var datasConvertidas = datas.map(data => {
    var [d, m, y] = data.split('/').map(s => parseInt(s));
    return new Date(y, m - 1, d);
});
 
var maior = new Date(Math.max.apply(null, datasConvertidas));
 
// converter de volta para dd/mm/yyyy
console.log(maior.toLocaleDateString('pt-BR'));
 
// ou, formatando na mão
function pad(val) {
    return val.toString().padStart(2, '0');
}
console.log(`${pad(maior.getDate())}/${pad(maior.getMonth() + 1)}/${maior.getFullYear()}`);

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