my shop uses a computer to take customer orders and upload them into
an online database. The workshop accesses the database online to view
the orders. when production is completed the workshop updates the
quantities used in the inventory online to allow the shop to see the
real-time quantities left.

Often, our internet service is out for a day intermittently.

What method, in detail, can i use to take orders offline and
synchronize with my online database so the workshop can also
synchronize with the database and get the latest orders. After
production is completed, the workshop pc can synchronize with the
online db & update the inventory.

Currently we have 4 pcs that use the site and all of them update with
similar and different types of information. We are using php & mysql
db. We have about 60 tables in the db & 300 php files.

store the data locally, then test for the connection with the central
db and perform a batch update periodically. or you could also use MS
Access at the client site and indirect replication...but I think the
cheapest way would be to get an ISP some a better QoS