plane mirror is in Y-Z plane

 speed of mirror , Vm =  - 2 ^i m /sec

 speed of particle , Vo  = 3 ^i + ^j + 4^k

from mirror and particle's vector form speed it it clear that both are moving in opposite direction in X axis......

 and  plane mirror is just moving in  X axis ..SO speed image of particle's image will change only in X-axis and will remain same in Y-Z  plane.

 so the speed of image  in X plane  = 2Vm + Vo 

                                                               =  2 ( -2^i ) +  3^i + ^j - 4^k

                                                               =  (- ^i + ^j - 4^k) m/sec