The question asked to factorise by grouping.
Your quadratic is 10x^2 - 11x - 6
You need to find two numbers that multiply to give 10*(-6) = -60 and add to give -11. The numbers are -15 and 4. So break the middle term into -15x + 4x to give
10x^2 - 15x + 4x + 6
You should now be able to factorise by grouping.
This thread's getting out of hand, so I'm going to close it off.
One way to give hints that don't give away the whole package is to analyze every step of the solution, and figure out exactly where the OP'er is stuck.
In this case, the OP'er knows he wants to proceed by the method of grouping. So the first thing to ask is where is the OP'er stuck. Once you know that, you can begin a gently leading Socratic dialogue such that, hopefully, the OP'er can answer each question and perhaps jump to the next conclusion before you ask the question to lead him there.
Remember John Milton Gregory's 6th Law of Teaching: "Excite and direct the self-activities of the pupil, and as a rule tell him nothing that he can learn himself."