{
    "_id" : 1,
    "item" : "ABC1",
    "description" : "product 1",
    "test" : {
        "colors" : [
            "blue",
            "black",
            "red"
        ]
    }
}

db.getCollection('mycollection').aggregate(
   [
      {
         $project: {
            numberOfColors: { $size: "test.$colors" }
         }
      }
   ]
)

Failed to execute script.

Error:
Assert: command failed: {
    "ok" : 0,
    "errmsg" : "The argument to $size must be an Array, but was of type: String",
    "code" : 17124
} : aggregate failed
_getErrorWithCode@src/mongo/shell/utils.js:23:13
doassert@src/mongo/shell/assert.js:13:14
assert.commandWorked@src/mongo/shell/assert.js:266:5
DBCollection.prototype.aggregate@src/mongo/shell/collection.js:1215:5
@(shell):1:1

Error: command failed: {
    "ok" : 0,
    "errmsg" : "The argument to $size must be an Array, but was of type: String",
    "code" : 17124
} : aggregate failed :
_getErrorWithCode@src/mongo/shell/utils.js:23:13
doassert@src/mongo/shell/assert.js:13:14
assert.commandWorked@src/mongo/shell/assert.js:266:5
DBCollection.prototype.aggregate@src/mongo/shell/collection.js:1215:5
@(shell):1:1