The Plane

$Equal\quad intercepts\quad mean\quad that\quad in\quad the\quad given\quad equation,\quad the\\ coefficients\quad of\quad x,y\quad and\quad z\quad should\quad be\quad the\quad same.\\ Out\quad of\quad all\quad the\quad options,\quad only\quad x+y+z=6\quad and\quad \\ 2x+2y+2z=5\quad have\quad equal\quad intercepts.$

$The\quad next\quad given\quad statement\quad is\quad that\quad the\quad plane\quad passes\\ through\quad (1,2,3)\quad i.e.\quad (1,2,3)\quad has\quad got\quad to\quad be\quad one\quad of\\ the\quad solution\quad of\quad the\quad equation.\quad Out\quad of\quad the\quad \\ selected\quad options,\quad only\quad x+y+z=6\quad fulfils\quad this\\ condition\quad as\quad 1+2+3=6.\\ So,\quad x+y+z=6\quad is\quad the\quad required\quad answer.$

Cheers!!:):)