"صَحيفة اَلْمُهَنْدِس كَبيرة وَقَديمة."
Translation:The engineer's newspaper is big and old.
Just make sure you put the 'al' by the noun (engineer) of the sentence, then by the adjectives describing that noun, and NOT by newspaper - so:
صحيفة المهندس الكبيرة والقديمة (Sahifat al-Muhandis al-kabiira wa-al-qadiima). This still implies possession of the newspaper, but possession of the Big,Old engineer Here we have the 'al' by the engineer, old and big, and not by the newspaper