In which sentence is the underlined phrase an adjective prepositional phrase? robert fulton’s invention of the steamboat gives him a prominent place in the history of transportation. robert fulton was born in 1765 in lancaster county, pennsylvania. robert fulton sailed on the seine river in a small paddle wheel boat. in 1807, the steamboat clermont traveled from new york city to albany in 32 hours.

Since you can't show underlining here, I will just discuss where in the sentences you can find an adjective prepositional phrase:
1) Robert Fulton’s invention of the steamboat gives him a prominent place in the history of transportation.
Here the prepositional phrases are: "of the seamboat" "in the history" and "of transportation"

2)Robert Fulton was born in 1765 in Lancaster County, Pennsylvania.
no adjective prepositional phrase here!

3) Robert Fulton sailed on the Seine River in a small paddle wheel boat.
no adjective prepositional phrase here!

4) In 1807, the steamboat Clermont traveled from New York City to Albany in 32 hours. no adjective prepositional phrase here either!