The correct answer to this open question is the following.
Unfortunately, you forgot to attach the map.
However, we can say the following. The present-day nations best represented in the areas where Islam had spread by 750 CE are Spain (most of the Iberian Peninsula), the southwest part of France. Of course, all the Arabian peninsula, the United Arab Emirates, Saudi Arabia, Qatar, Yemen, Oman, Iraq, Syria, Iran, Jerusalem, Jordan, parts of Afghanistan and Pakistan, and the region of North Africa, including Egypt, Morocco, parts of Argelia and Libya.
Islam spread during these years through trade, conquests, and evangelization. The Umayyads did not force conversion to Islam but tried to persuade people to embrace the Muslim religion. The Umayyads moved the capital from Mecca to Syria, in the Middle East.