If both layouts refer to the same Table Occurrence ( a table occurrence is one of the "boxes" in Manage | Database | Relationships), in Show Records From ( Layout setup...), modifying the field on one layout automatically modifies it on the other as they will both be referring to the same field in the same record.
If this is not the case, additional steps will need to be taken. I can't go into many specifics if that's the case as I don't know how you've set up your layouts and the relationships on which they are based. In general terms, you can use Set Variable, to put a copy of the current record's primary key in a variable and another set variable to hang on to the value you want to see on both layouts, Freeze the window, switch to the other layout, enter find mode, use set field to put the value from the variable in the appropriate field for this second layout, perform the find, use a second set field to copy the value from the second variable into the field where you want to see the value and then return to your original layout.
Another way is to make the field in question a field with global storage. Whith such a setting, you can change its value on any layout in your file and this new value will be visible on any other layout where you put this field.