JavaScript array not recognized

You are attempting to set an element in an array called ArrayName, which is not declared anywhere:

<script type="text/javascript">
   // You are attempting to access an array but it hasn't been declared:
   ArrayName['FirstValue']['SecondValue'] = {
   name = 'checbox_id'
   checked = true }
</script>

Your syntax indicates that this is an array that contains nested arrays, like this:

var ArrayName = [[1,2,3], [4,5,6], [7,8,9]];

So, if you wanted to get the number 8, you'd need to access the third array element and get the second value found in the array stored there with this syntax:

// Remember, array indexes start counting from zero
ArrayName[2][1];  // Get the third element's, second item

Or (if we take your example literally, where you are searching for literal strings that are not positive integers), ArrayName wouldn't be an array, it would be an Object that you are trying to access the property FirstValue of and this property then stores another object as its value and that object has a property called SecondValue. That structure would look like this:

var myObjectLiteral = {
  FirstValue : { SecondValue : something }
}

But, without knowing what you are trying to accomplish, we can't possibly help you write the array or the object.

Next, we have to talk about the object that you are trying to assign to the array:

{
       name = 'checbox_id'
       checked = true
}

This syntax is incorrect. You are missing a comma to separate on key/value pair from the next. It should be:

{
       name : 'checbox_id',
       checked : true
}