"Molly created an all natural laundry detergent that could be used for washing clothes at the age of thirteen." has a misplaced modifier. Because the modifier at the age of thirteen is adjacent to washing clothes, this sentence wrongly suggests that the washing clothes should only be done at the age of thriteen.

"Sarah saw palm trees and lizards on vacation in Florida." This sentence has a misplaced modifier. It wrongly suggests that the palm trees and lizards were on vacation.

"On vacation in Florida, Sarah saw palm trees and lizards. " This sentence does not have a misplaced modifier. This sentence correctly suggests that Sarah is on vacation in Florida. 

"Trying to fall asleep, the bed felt uncomfortably lumpy." This sentence has a dangling modifier. It wrongly suggests that the bed was trying to fall asleep.

"Before doing pluming work, the water should be turned off." This sentence has a misplaced modifier. It wrongly suggests that the pluming is doing pluming work.

When a sentence begins with a noun phrase + comma + another noun, there’s a good chance that it’s beginning with an appositive (noun used as a description) modifier. That is the case here: “a talented musician” is a description of the noun that comes after the comma, and the noun after the comma is the noun that performs the action in the verb (“John’s family proudly attended…”).  

Whenever you’re using a modifier, it must logically describe the noun that comes next to it. Here “a talented musician” is singular, describing one musician. But John’s family is more than one person, so the modifier doesn’t work. But “a talented musician, John” does work since John could logically be one talented musician. That answer corrects the singular-vs-plural logical errors in two answer choices and is therefore correct.

Note that “they were talented musicians, John’s family…” is not a modifier, since “they were talented musicians” has both a noun (they) and a verb (were). That answer choice has its own grammatical error, then, in that, you cannot simply split two clauses with only a comma.

A modifier is a word or phrase that modifies or describes, another word or phrase. A misplaced modifier is a modifier that appears to modify the wrong word or phrase because it is too far from the word or phrase that it should modify. “He was a tall man with long arms weighing 200 pounds.” has a misplaced modifier. Because the modifier “weighing 200 pounds” is adjacent to the arms, this sentence wrongly suggests that the man’s arms are remarkably heavy.

A modifier is a word or phrase that modifies or describes, another word or phrase. A misplaced modifier is a modifier that appears to modify the wrong word or phrase because it is too far from the word or phrase that it should modify. “Mr. Griffin served breakfast to the students on paper plates.” has a misplaced modifier. Because the modifier “on paper plates” is adjacent to the students, this sentence wrongly suggests that students who were sitting on top of paper plates would be served breakfast.

“He gave sandwiches to all the girls in plastic bags.” This sentence has a misplaced modifier. It wrongly suggests that the girls were in plastic bags. “I saw the car looking through the window.” This sentence has a misplaced modifier. It wrongly suggests that the car was doing the looking. “The boys saw all lions and tigers on the field trip to the zoo.” This sentence has a misplaced modifier. It wrongly suggests that the lions and tigers were the ones on the field trip. “I passed the piping hot-coffee to the man next to me.” This sentence correctly places the modifier to suggest the coffee, not the man, was piping-hot.

“To improve her essay, each paragraph was rewritten.” This sentence has a dangling modifier. It wrongly suggests the essay was somehow rewritten by itself. “He smelled the pizza driving past the restaurant.” This sentence has a misplaced modifier. It wrongly suggests the pizza was driving past the restaurant. “Justin drove to the stadium in his father’s car.” This sentence has a misplaced modifier. It wrongly suggests that Justin drove to a stadium that was located inside his father’s car. “While walking home, Megan called her father.” This sentence correctly places the modifier to make clear that Megan, not her father, was walking home.

“Looking toward the west, the sun was setting over the ocean.” This sentence has a dangling modifier. It wrongly suggests the sun was looking toward the west. “Jeff rode to school on a bus.” This sentence has a misplaced modifier. It wrongly suggests that the school was located on a bus. “The teacher gave an exam to students with only two questions.” This sentence has a misplaced modifier. It wrongly suggests that the students, not the test, had only two questions. “While he was driving past the restaurant, Greg smelled tacos.” This sentence correctly places the modifier to make clear that Greg was driving past the restaurant.

“I took my car to the repair shop with a broken headlight.” This sentence has a misplaced modifier. It wrongly suggests the repair shop had a broken headlight. “They watched the sunrise sitting on the beach.” This sentence has a misplaced modifier. It wrongly suggests the sunrise was sitting on the beach. “Hiking the trail, the birds chattered constantly.” This sentence has a dangling modifier. It wrongly suggests the birds were hiking. “Danny took a train to the airport.” This sentence correctly places the modifier to make clear that Danny, not the airport, took a train.