Option 1: Using a coordinating conjunction
* Hannah jammed her thumb, and Kayle almost broke her hip and elbow.
Option 2: Using a semicolon
* Hannah jammed her thumb; Kayle almost broke her hip and elbow.
Option 3: Using a conjunctive adverb
* Hannah jammed her thumb. Moreover, Kayle almost broke her hip and elbow.
Explanation
* Independent clauses are complete sentences with a subject and verb.
* Coordinating conjunctions (for, and, nor, but, or, yet, so) connect two independent clauses. They require a comma before the conjunction.
* Conjunctive adverbs (however, therefore, meanwhile, etc.) connect two independent clauses with a semicolon before the adverb and a comma after it.
Important Note: It's important to clarify that "Kayle almost broke her hip *and* elbow." This is more accurate than "her hip elbow" which doesn't make grammatical sense.