0-callbacks.js

var async = require('async');

async.eachSeries(array, function(item, callback){
    callAsyncFunction(item, function(error, data) {
        if (error) {
            return callback(error);
        } else {
            async.eachSeries(arrayTwo, function(sItem, sCallback) {
               count++;
               callAnotherAsyncFunction(item + sItem, function(error, data) {
                   if (error) {
                       return callback(error);
                   } else {
                       sCallback();
                   }
               })
            });
        }
    })
});

1-promises.js

function doSomething(item) {
  return callAsyncFunction(item).then(function(data) {
    return Promise.all(arrayTwo.map(sItem => doSomethingElse(item, sItem)));
  })
}

function doSomethingElse(item, sItem) {
  count++;
  return callAnotherAsyncFunction(item + sItem);
}

array.map(doSomething);

2-asyncawait.js

for (let item of array) {
  let x = await callAsyncFunction(item);
  for (let sItem of arrayTwo) {
    let y = await callAnotherAsyncFunction(item + sItem)
  }
}