g.js

function main(str) {
  var ssT = /[\*\+\-\/]/;
  var nsT = /\d/;

  var ns = str.split(ssT).filter(function(s) {
    return s !== '';
  });
  var ss = str.split(nsT).filter(function(s) {
    return s !== '';
  });

  console.log(ns);
  console.log(ss);
  var hasTimes = true;
  while(hasTimes) {
    hasTimes = false;
    for(var i = 0;i<ss.length;++i) {
      if(ss[i] ==='*') {
        hasTimes = true;
        ns.splice(i,2,parseFloat(ns[i]) * parseFloat(ns[i+1]));
        ss.splice(i,1);
        console.log(ns);
        console.log(ss);
        break;
      } else if(ss[i] ==='/') {
        hasTimes = true;
        ns.splice(i,2,parseFloat(ns[i]) / parseFloat(ns[i+1]));
        ss.splice(i,1);
        console.log(ns);
        console.log(ss);
        break;
      }
    }
    if(!hasTimes) break;
  }

  while(ns.length > 1) {
    for(var i = 0;i<ss.length;++i) {
      if(ss[i] ==='+') {
        ns.splice(i,2,parseFloat(ns[i]) + parseFloat(ns[i+1]));
        ss.splice(i,1);
        break;
      } else if(ss[i] ==='-') {
        ns.splice(i,2,parseFloat(ns[i]) - parseFloat(ns[i+1]));
        ss.splice(i,1);
        break;
      }
    }
  }
  return ns[0];
}

console.log(main("4+5+6+5/8*6"));
console.log(main("1+2/8*4-4"));