Answer: Making an earnest or desperate appeal
Explanation:
Doesn't exist or that is forbidden to be seen OR rare
Every gerund/participle ends in -ing, so you can know for sure that the answer is one of these two. Since here <em>turning </em>is used with an adverbial function (that is, it is basically an adverb - it tells us WHEN Kate bumped into David), the correct answer is B) participial.