How to solve this problem ?? Is the given solution correct?

There are 4 look-aheads.

1 from E->.T ($)

next one is again we are calling E->.E+T

hence again E->.T, but here first of next of E = + hence we got (+)

from T->.T*E next time we can get (*)

from T->.T-F next time we can get (-)