The minimum item level (ilvl) required for an item to have 6 sockets is 50. However, there are a few important exceptions to keep in mind:
Exceptions:
Strongbox Modifier: Items dropped from strongboxes with the "of Complexity" modifier can have more sockets than usual for their item level. So, an item with this modifier could have 6 sockets even if it has an ilvl lower than 50.
Crafting Bench: You can use the "Vorici’s White Socket" crafting recipe to add sockets to an item regardless of its ilvl. However, this recipe is quite expensive, requiring 350 Jeweller’s Orbs per use.
Unique Items: Some unique items are guaranteed to have a specific number of sockets, regardless of their ilvl. For example, the unique chest armour "Victario’s Influence" always has 6 sockets.
Additional Information:
The number of sockets an item has does not affect its chance of linking with Orbs of Fusing. That only depends on the item’s quality and the RNG of the process.
You can check the ilvl of an item by holding down "Alt" while hovering over it in your inventory or by typing "/itemlevel" in chat with the item on your cursor.