Which accomplishment of thomas jefferson is shown on the map as unorganized territory

The Louisiana Purchase

[You didn't show the map, but that's the probable answer.]

Explanation:

President Thomas Jefferson commissioned James Monroe and Robert Livingston to negotiate a deal with France to acquire New Orleans or all or part of Florida. When they went to France to negotiate, Monroe and Livingston found that Napoleon was ready to sell a much wider range of territory to the United States, to finance his European wars. Napoleon was asking $22 million for the whole territory that became the Louisiana Purchase. The US team negotiated the price down to $15 million.

Then there was a constitutional crisis back home: Did the President have the authority under the constitution to make such a major addition to the nation's territory and spend the nation's funds to do so? Jefferson himself initially thought a constitutional amendment might be necessary to authorize such a large action. Ultimately, Jefferson simply sought approval of the purchase from Congress. He used this analogy to describe what his administration was doing on behalf of the country: ""It is the case of a guardian, investing the money of his ward in purchasing an important adjacent territory; and saying to him when of age, I did this for your good."