Step 1: Recall the rule for modifying a verb.
In English, only an adverb can modify a verb. An adjective is used to describe a noun, not an action. This is the grammar rule we test the sentence against.
Step 2: Locate the verb in question.
In the phrase "were secure fastened", the word "fastened" functions as a past participle verb, telling us how the tiles were attached to the shuttle.
Step 3: Check the word placed before the verb.
The word "secure" sits right before "fastened" and is meant to describe the manner of fastening. Since "secure" is an adjective, it breaks the rule from Step 1. The manner of an action must be shown using an adverb, which here should be "securely".
Step 4: Confirm the other three choices are clean.
"Tiles" is a simple subject noun, "shuttle re-entered" is a correct subject-verb pair, and "atmosphere" is a correctly used object noun. None of these three break any grammar rule.
Final Answer:
Only "secure fastened" is wrong and needs to become "securely fastened", so option (b) is correct.