Question

allens new computer, a purchase he made with his tax rebate, has so many great apps that he could take over the world if he opened something besides the word processor.

remove the comma between rebate and has.
remove the comma between computer and a.
no change is necessary.
add a comma between world and if.

Explanation:

The phrase "a purchase he made with his tax rebate" is a non-restrictive appositive that adds extra, non-essential information about the computer. Non-restrictive appositives need to be set off by commas, so the commas around this phrase are correct. The clause "if he opened something besides the word processor" is a restrictive adverbial clause that directly modifies the main clause, so it does not need a comma before "if".

Answer:

No change is necessary.