In this case, "designed" is not a past tense verb. It's a participle, which means it's a verb that's functioning as an adjective. What it means is "the toner that was designed specifically for..." It describes the toner. This is a special toner "designed" specifically for a certain printer. Here are a few more examples of similar phrases with participles: "The clothing made by our company" (the clothing that our company made) "The man bitten by the dog" (the man who was bitten by the dog) "The cups filled with water" (the cups that have been filled with water)

'Designed' is not a past tense verb in this context. 'Designed' is part of the noun phrase which is the subject of the sentence. The whole phrase "The toner designed specifically for the PX300 laser printer" is the noun phrase. In this noun phrase, the word 'designed' is a participle functioning as an adjective. 'The toner designed for....' is a reduced form of the passive relative clause 'The toner which was designed for...'. . This is a very common construction in English. Take a look here for more information: https://www.perfect-english-grammar.com/participle-clauses.html

Q.The toner _____specifically for the PX300 laser printer should not be used with any other model.

And the answer is " designed" ,I wondering why use past verb? Both design (noun) and designed (past tense verb) can work in this sentence. BUT the meaning is different with each and the far more common usage would be "designed" and so that's why I would expect it as an answer. Example: If you want a toner "design"(noun) for a printer, that means you want the plans and procedures on how to make that cartridge. Whereas if you want a toner designed (verb) for a printer, that generally means you want a cartridge that has already been made/designed to work. The action of making or designing took place in the past.

Gray has given you the correct answer. 'Designed' is NOT a past tense.

It is past tense because the toner was designed at an earlier time, in other words, the toner is not being presently designed. If you are talking about a product and its qualities, then you will most certainly have to speak about it in the past tense because it has already been created. Hope this helps!