Desargues's Theorem says that if two triangles are drawn in perspective from a point, then the points of intersection of their corresponding pairs of sides are collinear.
To solve your problem, we need to end up with a diagram like the one attached. l and m are the two initial lines and P is the given point. Triangles ABP and FGH are the ones that will end up being in perspective from the point of intersection off the paper. The dotted line n is the one we need to find, and the line k represents the line joining pairs of corresponding sides.
To draw the diagram, draw the given lines l and m, and the point P. Then the line k (more or less anywhere); then the other points in alphabetical order. Start with A and B in arbitrary positions on the lines m and l. This fixes C, D and E. Then choose any convenient point for F. Then find G and finally H. Join PH to find the line n.
Hope that helps.