how can i find a value of a specified object property in an array using mongoose find

You need $ operator in this way:

db.collection.find({
  "totalCreatedForms.formName": "formtwo"
},
{
  "_id": 0,
  "totalCreatedForms.formIndex.$": 1
})

Find query has two objects.

The first to match the element you are looking for.

The second one is to indicate which fields returns. So, _id field will not be returned and, from array, only the index where the positional operator is placed, will be returned.

Ouput example is like this:

[
  {
    "totalCreatedForms": [
      {
        "formIndex": 1
      }
    ]
  }
]

Note that mongo is a data base who store documents and return documents, so this is the easiest way (without aggregation) to get only the value you want instead of the entire array.

Example here