You can learn to make drums with any alt at around level 100 in 5 minutes and two/three steps.
If you are coming here in order to find out how to learn to make drums on your alts, this is a step-by-step guide:

0. Skip this step and go to Step 1 if you do not want to go to Draenor and want to craft the Legion item using the Legion materials.
Obtain as many 生獸皮 as you need. You need at least 5x to learn the recipe. You can purchase them using Draenor Garrison resources in your Garrison or buy them using gold on the Auction House.

1. Learn Leatherworking from any Leatherworking trainer in any capital city:

2. You can now learn Legion Leatherworking in Legion Dalaran, which will immediately increase your Leatherworking skill cap to 800. You need to obtain 20x 石皮皮革 and 5x 雷鱗 - buy them on the Auction House, or learn Skinning and farm the items yourself. The vast majority of skinnable mobs in the Broken Isles will yield Leather when skinned and you can easily get the 5 Stormscales from e.g. any crabs in Aszuna. The quest is available at the Legion Dalaran Leatherworking trainer linked in step 1.
After quest completion you can also immediately purchase 圖樣：山脈之鼓 from 拉尼德‧怒金 and start making 山脈之鼓.
Stop here if that is all you care about, but note that Drums of Fury are cheaper to craft and the resources are free. Go to step 2.2 if you want to learn that recipe as well.

2.2. Go to Ashran and find your faction's Leatherworking trainer by asking a guard NPC.
A NPC next to them (加姆‧林行 for Horde and 安德斯‧隆斯提屈 for Alliance) will sell 德拉諾製皮 for roughly 100g less any faction discounts.
Purchase this and learn Draenor Leatherworking. Go to Step 2.3

2.3. You will have automatically learnt how to craft 德拉諾製皮奧秘 on a long cooldown. Immediately craft one using 5x 生獸皮, and now you can immediately purchase 圖樣：狂怒之鼓 at the same NPC.

Happy crafting!