Learn Russian: Если бы у нас был креативный менеджер, он предложил бы иную концепцию. - If we had a creative manager, he would propose a different concept.

Both mean "different" or "other," but иную (from иной) is slightly more formal and often implies a fundamentally different alternative. Другую (from другой) is more common in everyday speech and can simply mean "another one." Using иную концепцию emphasizes that the manager would bring a completely new way of thinking.

What case is иную концепцию in, and how do you decline this pronoun?

It is in the accusative case because it is the direct object of the verb предложил (would propose). The dictionary form is the masculine nominative иной. Even though it is classed as a defining pronoun, it declines exactly like a standard adjective with a stressed ending (like молодой). The feminine accusative form is therefore иную.

Why are the verbs был and предложил in the past tense if this is about a hypothetical present situation?

In Russian, unreal conditionals (situations that are hypothetical or contrary to fact) always use the past tense form of the verb paired with the particle бы. The combination of если бы plus the past tense can refer to the past, present, or future depending on the context.

Could the particle бы in the second half of the sentence be placed somewhere else?