The feature/cantrip descriptions says nothing about their dice can not stack:
... use a bonus action on your turn to choose one creature other than yourself within 60 feet of you who can hear you. That creature gains one Bardic Inspiration die, a d6. Once within the next 10 minutes, the creature can roll the die and add the number rolled to one ability check, attack roll, or saving throw it makes.
You touch one willing creature. Once before the spell ends, the target can roll a d4 and add the number rolled to one ability check of its choice.
That feels wrong to me, since a pair of 1-level characters can have ridiculously high (up to +10, +6 average) bonus to an ability check.
To my knowledge, bonuses in D&D 5e (advantage, proficiency bonus, etc.) do not stack, hence the question. Can a player use both Bardic Inspiration die AND d4 from Guidance for the same check?
I've found a related question, but it is about 3.5e.