There are few options on how to complete this quest.

Option 1.
Find or in grenade boxes .
Those are active grenades that explode on contact with surface after 0.3 seconds delay. A fool-proof mechanism is in place so a minimum distance of 5 meters is required. If you are not familiar with those mechanics - better to test in offline mode first.
Next we go to Factory . Select a nade, cook it and wait for enemy in narrow corridors.
It is best to look for grenades in these locations:
On the map Reserve
On the map Lighthouse
On the Streets of Tarkov

Option 2.
Get any armor with hand protection and full helmet (which protects your whole head). Get some nades with you (preferably , but is alright too). If you have lots of cash - or will be better due to lowest explosion timer. Next step is again - Factory ! Play map as normal, but when you meet someone with no armor/low tier weapon or a hatchling, shoot their legs and try to finish them off with a nade.

If you've hear any automatic rifle or shotgun fire - high chance this is a boss and he doesn't like nades being thrown, so better bail quickly (or kill him if you are confident!). Always carry with you for quick getaway.

Option 3.
If you don't like active gameplay or Factory is not a map of your likings, there is always an option of carrying few cheap nades ( or ) with you every raid. Try to use them often when fighting other players and eventually you will complete it.

Kills with , , and are not counted