A grinding noise each time a gear is selected in a manual vehicle points to

Correct answer to question 71 (Auto & Shop Information): worn synchronisers or a clutch not fully releasing

Method

Synchronisers match the shaft speeds before the gear teeth meet, so when they wear the teeth clash. The same noise appears if the clutch does not release fully, because the gearbox input shaft is still being driven. Both causes sit in the same part of the drivetrain, which is why the noise alone does not identify which.