Fill in the blank with the correct phrase from the options given belo…

The correct answer is Option (1) → actually, but

Conjunction of contrast:

• But joins two ideas that contrast with each other.
• Actually (in fact) stresses that the flowers really can stay unseen for so long.
• This sentence: the flowers stay invisible for years, but then appear suddenly after rain. Only this option puts a contrast word in the joining position.
• Complete sentence: Desert flowers can be invisible for years, actually, but appear suddenly after heavy rain.

Why the Other Options are Incorrect?

Option 2: alternatively or — Incorrect. "Alternatively" and "or" offer a choice between two possibilities. The flowers do not choose between being invisible and appearing, one follows the other.
Example: You can go by train or by bus.

Option 3: consequently and — Incorrect. "Consequently" shows a result, and "and" only adds. The flowers do not appear as a result of being invisible, so the contrast is lost.
Example: He missed the bus and consequently was late.

Option 4: nevertheless, so — Incorrect.

• "Nevertheless" shows contrast, but "so" shows a result.
• The two together clash and cannot join the two halves.
  Example: It was raining; nevertheless, the match went on.

Contrast: "but" and "nevertheless" show contrast, "so" and "consequently" show a result, and "or" and "alternatively" offer a choice.