Yes, absjbk29's translation is correct and the one given in this lesson is unequivocally wrong. In most instances Duolingo tends to mark things wrong if you deviate from their expected word order. Here it's not just the word order that I disagree with, it's the literal meaning.
In Victorian times there were big questions of etiquette around who you would introduce first to whom. I guess most Israelis aren't so formal, but we still need correct translations.
No, that's not the verb in question. לייצג is pi'el and this is a hif'il skill, so the infinitive of this verb is להציג. Also, the masculine form is different.
pi'el - infinitive - לייצג, masculine sg. מייצג, feminine sg. מייצגת
pealim link: https://www.pealim.com/dict/837-leyatzeg/
hif'il - infinitive - להציג, masculine sg. מציג, feminine sg. מציגה
pealim link: https://www.pealim.com/dict/870-lehatzig/
One note. Even though they are from the same root, they don't mean the same thing. לייצג means "present" in the sense of representation, not introduction, as the hif'il verb does.