Learn Russian: В данный момент директор занят. - At the present moment the director is busy.

Данный literally translates to the English word given, as it is a participle derived from the verb дать. However, in professional or formal contexts, it is widely used to mean current or present. В данный момент is a standard set phrase for currently, which fits the formal office setting better than the simpler в этот момент.

Is the phrase в данный момент in the Prepositional or Accusative case?

It is in the Accusative case. In Russian, exact points in time using the preposition в take the Accusative. Because момент is a masculine inanimate noun, its Accusative form is identical to its Nominative form.

Why is the short-form adjective занят used rather than the long-form занятый?

Short-form adjectives are strongly preferred for describing temporary states. Because the director is only busy right now rather than being a permanently busy type of person, the temporary short form занят is required.

Why does the time phrase в данный момент come at the very beginning of the sentence?

In Russian, sentences typically flow from the background context to the most important new information. Starting with В данный момент sets the scene, placing the core news—the fact that the director is занят—at the very end of the sentence for emphasis.