"Mężczyzna" is masculine (although it ends with "-a"), "tę" would be used with feminine nouns. E.g. "Słyszę tego mężczyznę. Słyszę tę kobietę" = "I hear this man. I hear this woman".
I give up. Gotta take a break. These lessons and repetitions are not helping me understand all thisbten, ta, to, czu, tego, tamtego, tamci....ay ay ay!