Learn Arabic (Modern Standard): حدث ركود عالمي، وبناء على ذلك أعلنت الشركة إفلاسها. - A global recession happened, and accordingly the company announced bankruptcy.

Literally, it translates to 'based upon that' (بناء means 'building' or 'basis'). While لذلك means a simple 'so' or 'therefore', بناء على ذلك is a bit more formal. It emphasizes that the second action was a direct, logical decision or consequence built upon the first event.

How is بناء pronounced here, and why doesn't it have an extra letter for the 'an' sound?

It is pronounced binā'an. It takes the 'an' ending (tanween fatha) because it acts as an adverb in this phrase. You will usually see it written with the two small strokes above the hamza (بناءً). It does not take an extra alif at the end because Arabic spelling rules state that a hamza at the end of a word shouldn't be sandwiched between two alifs.

Why does the verb أعلنت come before الشركة in the second half of the sentence?

Arabic strongly prefers Verb-Subject-Object order. After an introductory or transitional phrase like وبناء على ذلك, it is most natural to immediately follow with the verb أعلنت (announced) before the subject الشركة (the company).

Why does the word for bankruptcy (إفلاسها) end with a feminine suffix?

The suffix ـها translates to 'her' or, in this case, 'its'. It refers back to الشركة (the company), which is a feminine word. In Arabic, you must match the possessive suffix to the gender of the noun that possesses the item.