Hello Asmaa,

I've checked the issue and here's what you can fix,

1) You need to remove '_' at beginning of compute parameter and write 'compute' instead as '_compute' is not a valid parameter.

2) The arguments used for onchange() decorator must be simple field names. If dotted names are used then it will be ignored by the decorator. Your onchange() decorator: ('deliver_id.shipping_method') will be ignored.

3) If your onchange method (in your case x) returns more than one value It throws an error, you cannot use them to write in Many2one as you can write only one value at a time in Many2one. 

So if your field 'allowed_value_ids' is not used in the view or anywhere else other than in the domain of field 'city', you can make the field type 
of field:'allowed_value_ids' as Many2many instead of Many2one.

Ex:- Suppose you have 3 cities, compute on your field 'allowed_value_ids' returns 2 cities, so it will write those two values in field 'allowed_value_ids' if it is a Many2many but not in Many2one. Now field 'city' will filter only those cities which are there in the field 'allowed_value_ids'. 

Hope this will help you.

Thanks & Regards,
Email: odoo@aktivsoftware.com
Skype: kalpeshmaheshwari