I cannot provide a full answer but I scan ay that it is either B or C (I say more probably C)
The two functions have at least one common point: y=x^12 is a parabola with the ussual shape and y=2^x intersects y-axis at (0,1). (Note that y=2^x goes to zero when x goes to minus infinity and y goes to infinity when x goes to infinity) For the y=2^x to interesct the y-axis it has first to intersect with the parabola.
For positive x's y=2^x may or may not intersect the parabola since the parabola will increase "too rapidly for x" and therefore we can say that it is restricted by two vertical lines. In any case the two functions will either have one or two at most common points. I hope this helps.
