What is the average number of magic items for a level 6 character in D&D 5e Adventurers League? Such as, 1 rare, 2 common, 1 uncommon, etc.
Talk to your DM
Character creation with a new DM is going to rely on their decisions about what you can use.
While they may allow you to transition your current character, they may also not if the campaign isn't yet at that level or for any other reason (like not allowing multiclassing.)
About one uncommon, half a dozen consumables
Note: According to the body of the question, and the dnd-adventurers-league tag, your question is about what number of items a 6th level character in AL would typically have. There seems to be some history/evolution of the question. I am answering the question that is currently posted.
How many items a player character owns will depend on many factors like which adventures they played and what items they found or missed there and how that loot was split. AL to my knowledge does not publish statistics on this, so we do not know how the distribution looks like.
However, the player rules give some useful indication. They state:
You may keep as many magic items as you are awarded but must limit the number of magic items you bring on an adventure based on the table below.
CARRIED MAGIC ITEMS BY TIER
Tier Uncommon+ Common Consumable 1 1 5 5 2 3 5 10
Uncommon, rare, very rare, legendary, and unique permanent magic items are included in the “Uncommon+” column. Common permanent magic items are included in the “Common” column
This is not exact for level six, but it gives us a cap: at most a level six character could bring 18 magic items to the table, most of them consumables.
Level six is at the lower end of tier 2, so it is much more likely that the number of items would be closer to tier 1: 1-2 Uncommon+, 5 common, maybe 6-7 consumables.
The AL DMG for Forgotten Realms states that characters can buy spell scrolls
Spell Scrolls. Characters can purchase spell scrolls during an adventure if the NPC has access to the spell; lower-level (1st and 2nd level) spell scrolls may have multiples available for purchase;
If they buy those, the number of consumables might be closer to the upper bound.
As Uncommon+ can be higher rarities, it also might be possible that they found a rare item in one of the adventures and have that instead of the uncommon. (The AL DMG limits rolled random items in tier 2 to at most Rare rarity).
There is guidance for starting a character on level 5. This is very close to level six, and while such a character can be expected to have fewer items than one that was played and leveled up, it gives us a lower bound. The rules say:
As a 5th level character, you may choose one of the following magic items to possess in addition to your standard gear from your class and background.
This is followed by a list of uncommon items like +1 weapons or armor, wand of the war mage, arcane grimoire, or a bag of holding.
So the lower bound for a level six character would be one uncommon item.
Common permanent items
There are only three Common magic items in the DMG, and all of them are consumables (potion of healing, potion of climbing, spell scroll level 1). Most permanent Common items are introduced in Xanathar's Guide to Everything, which says about them:
These items seldom increase a character's power, but they are likely to amuse players and provide fun roleplaying opportunities.
Xanathar's is legal. These items likely are mostly for "color" (you can also see that by the number not changing across tiers, all the way up to tier 4 it stays at 5), and will not impact the characters power.
In conclusion, something around one uncommon item and half a dozen consumables like healing potions and low-level scrolls sounds about right for level six. It might be a bit more, with the occasional rare item or second uncommon instead, or a couple more healing potions and scrolls. Flavor with up to 5 common permanent items.