。
I can't forget to meet her.
Literal
Not-forget-[without-ず] her [dat-に] meet-[must-なければならない]
The double-negative structure is characteristic: 忘れずに ('without forgetting') + ~なければならない ('must do'). Literally 'must meet her without forgetting' = 'must not forget to meet her.' Japanese often stacks negatives this way where English would use a single 'must not forget to'.