Age of Empires IV: Anniversary Edition

By far the easiest way to ensure Mongols can't reach your city is by building an additional layer of stone walls in front of your outer city. You should have more than enough time and resources (from two stone deposits, the starting one and the one to the south-west) to build a nice defense line.

All directions will refer to the default camera angle.

You have to cover 3 parts. The most obvious is the gigantic wall that you'll build from river to river (in more or less a straight line). The other one is to cover the bridge at the top of your base. Finally build a small wall from your south stone walls to the river. You won't be able to cover the south bridge with walls so just make sure you leave few crossbowmen on it to take care of small party later on during the mission.

Now to defences. Build towers and one gate. I was attacked more from the northern road (on the eastern part of your city) so I added a keep behind it. Recruit a lot of archers and crossbowmen, don't forget about upgrades. Leave 3 villagers idle to repair walls as soon as they are damaged. As soon as Mongols find out that the gigantic wall was not part of the script you'll be attacked by siege rams from the very beginning. They aren't too bad, by now you should have more than enough experience with turtling. I kept a small spearmen party to take care of any unattended rams. Make sure to move ranged units that protect your inner city to the front line, your city won't be attacked (except the small vanguard party mentioned earlier).

After you defend against all their waves you'll be attacked by a gigantic army. You won't be able to survive this (trebuchets...) but you need to steal enough time so your villagers can run away. Wait until Mongols destroy your stone wall and throw your units into the gap to steal few more seconds. It should be enough to give your villagers enough time which will complete the mission.

If done correctly Mongols won't even touch your wooden pallisade.