The B408 heads North-South between Hammersmith and Shepherds Bush in West London, providing an alternative to the A219 Shepherds Bush Road further to the West.
The road starts on the two-way section of the A315 King Street to the west of Hammersmith and heads North along Dalling Road. However, this road is one-way Southbound only, so in order to enter the road, either take the one-way Eastbound (but heading North at this point) A315 Studland Street (the route you would take if coming from Hammersmith) then left and right, via a short section of Glenthorne Road, or up the unclassified Ravenscourt Road (your more likely choice if approaching from the direction of Chiswick).
Dalling Road changes its name to Paddenswick Road before meeting Ravenscourt Road. It then reaches a double-roundabout crossing of the A402 Goldhawk Road, where you go left then right, after which the B408 continues up Askew Road until its classification terminates on the A4020 Uxbridge Road.
The road continues unclassified, though with some significance, as Old Oak Road, where it crosses the A40 at Savoy Circus (users of the A40 certainly know this junction, especially as it holds up the Westbound traffic badly) and splits the Westway and Western Avenue, as well as being the border of the Boroughs of Hammersmith & Fulham and Ealing. There it continues further to become Old Oak Common Lane and meets Old Oak Lane (the A4000) - a lot of roads that start Old Oak, easy to confuse....