You should have no probe using the multimeter.
First, set it to measure voltage. There is usually a '20VDC' setting (ie: it can measure up to 20V DC (direct current)). And you have your two probes, red and black.
At the back of the headlight, locate the plug that connects to the globe, and wiggle-jiggle it off. You'll see the 3 terminals in the plug. Check which terminal connects to the grey/black wire (grey wire, with black stripe); this is the positive power supply wire for the main beam. Check which terminal connects to the black wire; this is the negative power wire, connected to the earth point above.
Next, check the voltage at the battery, for reference. With your multimeter, touch the tip of the red probe firmly against the positive terminal/battery post, and hold it there. Then touch the tip of the black probe firmly against the negative terminal/battery post. Read what the voltage is; let's say it's 12.13V.
Next, turn the headlights on (with the plug disconnected from the passenger side globe). Ensure the driver's side headlight has turned on. Now, back at the plug of the passenger side, carefully put the tip of the red probe onto/into (you may be able to gently jam it into the end of the terminal) the terminal for the grey/black wire in the headlight plug. Then, carefully put the tip of the black probe onto/into the terminal for the black wire. Read the voltage.
If everything is working, it should read very close to the voltage of the battery. Ideally, it would read 12.13V (for example), but because the wiring has resistance, you would expect it to be a little less, say 12.03V.
If it's 0V/no reading, clearly this confirms there is an issue with the power going to the globe. We are expecting it to be 0V, but part of the process of elimination is confirming this is the case.
Next, move to the fuse board. Turn the headlights off at this stage. Locate fuses 10 and 11, and pull them out, exposing the terminals they connect into.
You need to then place the black probe onto a suitable ground point nearby (bare metal connected to the chassis). It might work to jam it into the metal door striker 'knob' screwed to the B-pillar; it might work jamming against the steering column; it might work jamming it against the ignition key barrel.
Once the black probe is grounded, you can then use the red probe to touch the fuse terminals. Turn the headlights on. Because you know the driver headlight works (it won't come on because you've removed the fuse), the terminal should become live, and show 12V, thereabouts. Fuse 11 connects with two terminals, orientated one above the other. One of them should show 12V (ie: power coming via the stalk switch and relay), though the other will show 0V (ie: coming back from the headlight globe which has no power at the moment). Confirm that one of the terminals for fuse 11 has 12V (it should be very close to the battery voltage, like 12.13V).
Now, probe the terminal next to it, from fuse 10. Ideally, this should also show 12V, thereabouts.
If so, then power is reaching this point, but not going to the plug on the passenger side. Thus, the fault must lie either with the fuse, or between the terminal and the plug (ie: along the wire).
Go this far, and let us know your findings.