So contrary to what you may believe, 3:4 is not 3/4 here, but rather "3 equal parts to 4 equal parts", which is a total of 7 equal parts. In short, the question is asking you to put point P 3/7 of the way from A to B (or 4/7 of the way from B to A, but we will do the prior.)
So firstly, how far apart is -9 from 5 (the x-coordinates)? That would be 14 units. Multiply 3/7 by 14:
[tex]\frac{3}{7}\times \frac{14}{1}=\frac{42}{7}=6[/tex]
Next, how far apart is 9 from -2 (the y-coordinates)? That would be 11 units. Multiply 3/7 by 11.
[tex]\frac{3}{7}\times \frac{11}{1}=\frac{33}{7}[/tex]
Now, since from -9 to 5 you are increasing, add 6 to -9:
[tex]-9+6=-3[/tex]
-3 is P's x-coordinate.
Next, since from 9 to -2 you are decreasing, subtract 33/7 from 9.
[tex]\frac{9}{1}\times \frac{7}{7}=\frac{63}{7}\\\\\frac{63}{7}-\frac{33}{7}=\frac{30}{7}[/tex]
30/7, or 4 2/7 is P's y-coordinate.
Putting it together, P's coordinate is (-3, 30/7).
