Among the many breeds of dogs that have developed over the last two

(a) Among the many breeds of dogs that have developed over the last two centuries, some have been bred for specific tasks like herding or guarding owners

like cannot be used to introduce examples

(b) Between the many breeds of dogs that were developed over the last two centuries, specific tasks have been bred into some, such as herding or guarding owners

among many breeds of dogs is correct , we use between if there were only two different breeds of dogs
specifics tasks were not bred; the dogs were bred- modifier/meaning error

(c) Many breeds of dogs have developed over the last centuries, some for specific tasks like herding and guarding owners.

like cannot be used to introduce examples of different tasks

(d) Over the last two centuries, many breeds of dogs have been developed, some for specific tasks such as herding or guarding owners

such as correctly describes the examples herding or guarding owners,
the modifier "over the two centuries" satisfies the questions what has or what is? that is what has happened over the two centuries?- ans many breeds of dogs have been developed!

and the modifier "some for specific such as herdig or guarding owner"-- what does this phrase refer to? "some breeds of dogs"

Is the correct option!

(e) Among the many breeds of dogs that had developed over the last two centuries, specific tasks such as herding or guarding owners have been bred into some

use of had is wrong there is no other event that took place in the past after the development,
again the specific tasks were not bred