[Haskell], 62 bytes

import Data.List a!b=[unwords.zipWith(++)r<$>transpose b|r<-a] 

[Try it online!] Usage:

Prelude Data.List> [["a","b"],["c","e"]]![["f","g"],["h","i"]] [["af bh","ag bi"],["cf eh","cg ei"]] 

This is quite similar to my answer to non-symbolic matrix multiplication: a!b=[sum.zipWith(*)r<$>transpose b|r<-a], substituting the multiplication (*) with string concatenation (++) and sum with unwords which concatenates a list of strings with a space in between. The import is needed for the transpose function, so all in all the transposition of the second matrix uses up half of the bytes ... [Haskell]: https://www.haskell.org/ [Try it online!]: https://tio.run/nexus/haskell#JYwxT8MwEEZ3fsVXqwOojcXI0FaqYGBgQGJgiDI4ybU@4drW@UKkqv89GNjee8PjS06ieE5RJQV7zDnw4JS/CU2DSDTSiFMS7NYHzJ4HDy7IQoWigiNeXfmiEPBkH/EuFKaRFv6fvjh19o2L3rlVv2@nOCcZi71y/mT195vNg9Srioslp0Lob7JrXLdcXP3ukSf9UIFF8WnGGm1rnNma3nTb1gyVyHQdVr/9VO38130lrn35AQ "Haskell – TIO Nexus"