Yes, you can, but typically how this is done is to split the mdb into parts. The tables reside in one .mdb in a shared folder somewhere & the queries, forms & reports live in a client-only version of the database. The client verison contains links to the tables in the 'back-end' database. Use File -> Get External Data -> Link... to connect to the back-end tables.
Each user has a local copy of the 'front-end', but they all share the common 'back-end'.
You could try the simplest thing: Tools -> Options -> Advanced -> Default Open Mode & check that it is set to Shared and that both Open databases using record-level locking and Edited record checked , but my experience just doing this in a multi-user environment is mixed. Sometimes works, sometimes not.
Taking a look at your image: if the form field in question maps to the same database record, then no, you can't have 2 people edit this at the same time. If the field maps to different records, then yes, it's possible.
Yet another update
If you have Access 2003 or similar there is a Database slpitter utility provided. Select Tools -> Database Utilities-> Database Splitter. It will ask for a location to save your files. You'll want this to be a shared drive. It should automatically make the linked tables for you and copy all your table data to a new 'back-end' database named
whatever your db name is_be.mdb.