The difference between "go down" and "come down". The way I understand it is that "come" is used when you are moving in the speaker's direction. You are going in the direction of the person you are addressing. Example: My friend wants to meet me at a cafe. I'm running a tad late so he calls. It's more fit to say "I'm coming." In that way, if the speaker asks a question using "come" it implies that the speaker is present in the place you are moving to. For example, my grandmother asks me if I am coming to church. It implies that my grandmother is at church or currently going to church. "Go" implies that you are not meeting with the speaker or moving in a different direction from where the speaker is. For example, In the example with my grandmother. If she asks if I'm going to church, it implies that she is not at church. And my friend says, "Go to the cafe." In most cases it would mean that she is not at cafe. But if she said "Come to the cafe." I would assume that she is at the cafe. To conclude, "Come" is used with motion towards the speaker, "go" with motion away from the speaker. Regarding your correction, I think your statement was correct. Since it's your friend, no need to be very formal or use "big words". "I would love to go with you but I can not, because I also have an event to go to on that day."