Based on the map what fraction or percentage of Europe and North Africa was initially controlled by the Axis powers in 1939 and what was the
change by 1942?

The Axis controlled most of Northern Africa: from Morocco to Libya, however, they never controlled Eygpt, which was kept under British Control.

In East Africa, Italy was developing a colonial empire: it controlled Ethiopia, Eritrea, Djibouit and Somalia. However, and this was a major change by 1942, the British conquered a portion of Somalia that was later known as the "British Somaliland".

By 1942, allied troops were advancing in Morocco and Algeria, while Axis troops, mostly German, were landing in Tunisia.

This campaign and the axis control of Northern Africa would only end in the following year: 1943.

d. migration