The correct answer is B: meet her?. The construction 'would like to' is always followed by the bare infinitive form of the verb. Hence 'would you like to meet her?' is grammatically correct.
A.meeting her?
B.meet her?✓ Correct
C.met her?
D.meet with her?
Explanation
The construction 'would like to' is always followed by the bare infinitive form of the verb. Hence 'would you like to meet her?' is grammatically correct. 'Meeting' (gerund) and 'met' (past tense) are wrong forms after 'to'. 'Meet with' is used in formal contexts for arranged meetings, but the simpler 'meet her' is most appropriate.
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