JSFiddle - React, Tailwind, and code Playground

JavaScript

var array = [{
      "date": '1-Jan-2015',
      "count": 4
    }, {
      "date": '4-Jan-2015',
      "count": 3
    }, {
      "date": '1-Feb-2015',
      "count": 4
    }, {
      "date": '18-Feb-2015',
      "count": 10
    }]

console.clear()

var result = array.reduce(function(ar, item) {
  var index = item.date.split('-').slice(1, 3).join(', ') //getting date Month-Year
  _item = ar.filter(function(a) {
      return a.date === index
    })[0] // getting item if already present in array
  indexOf = ar.indexOf(_item) // getting index of _item if _item is already present
  if (indexOf > -1)
    ar[indexOf] = {
      date: index,
      count: _item.count + item.count
    } // we sum the count of existing _item
  else
    ar.push({
      date: index,
      count: item.count
    }) // we push a new _item
  return ar
}, [])

console.log(result)
document.write('<pre>' + JSON.stringify(result, null, 2) + '</pre>')