Find the distance between the two points, using the Distance Formula.
Find the slope of the line through the two points, using the slope formula.
Pick one of the points (it doesn't matter which) and, using also the slope you just found, find the line equation.
a) Since one distance is twice the other distance, then the length of the segment is divided into three parts, two of which go with point A and the other with point B. The unknown points are of the form (x, y) = (x, mx + b). Plug this form (using the values of m and b that you obtained above) into the Distance Formula, with the distance of (x, mx + b) from A being twice (times 2) the distance from B.
Square both sides, and solve the resulting equation for x. Plug these x-values into your line equation to obtain the corresponding y-values.
b) This one works just line (a), other than dividing the length of the segment by 4 rather than by 3.
If you get stuck, please reply showing your steps and reasoning so far. Thank you!