You could use array's filter() function:

function filter_dates(event) {
    return event.date == "22-02-2016";
}

var filtered = events.filter(filter_dates);

The filter_dates() method can be standalone as in this example to be reused, or it could be inlined as an anonymous method - totally your choice =]

A quick / easy alternative is just a straightforward loop:

var filtered = [];
for (var i = 0; i < events.length; i++) {
    if (events[i].date == "22-02-2016") {
        filtered.push(events[i]);
    }
}

You can use the Array.prototype.filter method:

var newArray = homes.filter(function (el) {
  return el.price <= 1000 &&
         el.sqft >= 500 &&
         el.num_of_beds >=2 &&
         el.num_of_baths >= 2.5;
});

Live Example:

var obj = {
    'homes': [{
            "home_id": "1",
            "price": "925",
            "sqft": "1100",
            "num_of_beds": "2",
            "num_of_baths": "2.0",
        }, {
            "home_id": "2",
            "price": "1425",
            "sqft": "1900",
            "num_of_beds": "4",
            "num_of_baths": "2.5",
        },
        // ... (more homes) ...     
    ]
};
// (Note that because `price` and such are given as strings in your object,
// the below relies on the fact that <= and >= with a string and number
// will coerce the string to a number before comparing.)
var newArray = obj.homes.filter(function (el) {
  return el.price <= 1000 &&
         el.sqft >= 500 &&
         el.num_of_beds >= 2 &&
         el.num_of_baths >= 1.5; // Changed this so a home would match
});
console.log(newArray);

This method is part of the new ECMAScript 5th Edition standard, and can be found on almost all modern browsers.

For IE, you can include the following method for compatibility:

if (!Array.prototype.filter) {
  Array.prototype.filter = function(fun /*, thisp*/) {
    var len = this.length >>> 0;
    if (typeof fun != "function")
      throw new TypeError();

    var res = [];
    var thisp = arguments[1];
    for (var i = 0; i < len; i++) {
      if (i in this) {
        var val = this[i];
        if (fun.call(thisp, val, i, this))
          res.push(val);
      }
    }
    return res;
  };
}

You can do it with Array.filter

var data = [{
    "id": 1,
    "term_id": 5,
    "type": "car"
  },
  {
    "id": 2,
    "term_id": 3,
    "type": "bike"
  },
  {
    "id": 3,
    "term_id": 6,
    "type": "car"
  }
];

var result = data.filter(function(v, i) {
  return ((v["term_id"] == 5 || v["term_id"] == 6) && v.type == "car");
})

console.log(result)