Which layer does a continuous effect that changes a permanent's type apply in?

Continuous effects that modify a permanent's type, subtype, or supertype are applied in Layer 4, known as the Type layer. This is defined in Comprehensive Rules 613.1d, which states that type-changing effects are applied in this layer. Examples include effects that make a land also an artifact, or that change a creature into a non-creature permanent.

The seven layers, in order, are: Layer 1 (Copy effects), Layer 2 (Control-changing effects), Layer 3 (Text-changing effects), Layer 4 (Type-changing effects), Layer 5 (Color-changing effects), Layer 6 (Ability-adding/removing effects), and Layer 7 (Power/toughness-changing effects). Each continuous effect is applied in exactly one layer, and they are applied in this sequence to determine a permanent's final characteristics.

Understanding layers matters because effects in earlier layers can influence how later layers apply. For instance, if an effect in Layer 1 (a copy effect) changes a permanent into a different card, that new base type is established first, and then any Layer 4 type-changing effects are applied on top of that result.

Concrete example: The card Liquimetal Coating has an ability that reads 'Target permanent becomes an artifact in addition to its other types until end of turn.' This is a type-changing effect and is applied in Layer 4. If your opponent's Plains becomes an artifact land, that change is processed in Layer 4, after copy and control effects but before color and ability changes.