사라지다 is vanishing — someone leaving the stage, memories going, food disappearing. The -게 slot gives the manner: 멋지게 (stylishly, like dust after a performance), 희한하게 (oddly), 나도 모르게 (without my even noticing). 어떻게 사라져 is the bewildered version, 'how am I supposed to disappear?'.