"my acquaintance with" = "mi contacto con". See explanation below taken from Advanced Oxford Dictionary:

acquaintance {speaker} noun
1 [C] a person that you know but who is not a close friend:
Claire has a wide circle of friends and acquaintances. • He’s just a business acquaintance. • I bumped into an old acquaintance on the train.
2 [U, C] ~ (with sb) (formal) slight friendship:
He hoped their acquaintance would develop further.
3 [U, C] ~ with sth (formal) knowledge of sth:
I had little acquaintance with modern poetry.
 
meanings 2 and 3 correspond to the use in the phrase provided by you.
Good luck.


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Note added at 2002-11-05 16:31:21 (GMT)
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Me gustaria extender mis contactos con gente de Latinoamérica/ gente lationaomericana/lationamericanos.

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Note added at 2002-11-05 17:33:10 (GMT)
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Another possible translation of the phrase:
\"Me gustaría conocer más a la gente latinoamericana.\"

Meaning 3 applies here