This is a question from Oscillations chapter physics. You need to have your base very strong to attempt this question successfully. Your dynamics and Kinemetics concepts should be very clear. Projectile motion, force, laws of motion, these chapters and their formulas should be thoroughly known. And once you do, surelt practice such questions as they increase your confidence and also expose you to the type of questions to be asked in the competitive exams.

So now coming back to your question, here's the solution. The answer is it will take 1 second time. I'll show you how -

Since the particles begins its SHM from extreme it will already have difference of 90o

⇒X=Asin(ωt+90o)

X=Acos(ωt)

Now, Time period (T)=6=ω2x

⇒ω=3π

At X=2A

⇒2A=Acos(3πt)

⇒cos(3πt)=21

⇒3πt=3π

⇒t=1sec

Best wishes buddy. Thankyou.