By way of explanation I'll briefly explain each of the six days.
Sensho (先勝) means good luck before noon, bad luck after noon. It is also a good day for starting something new. Just make sure you start it before noon.
Senbu (先負) which is the opposite of above, bad luck before noon, good luck after.
Tomobiki (友引) literally means to 'pull a friend'. You never, ever want to have a funeral on a Tomobiki day. It would be like your friend is pulling you into the grave. Very bad luck indeed!
Bustumetsu (仏滅) refers to the day Buddha died, so bad luck all around. This is pretty much an unlucky day for anything. You don't schedule anything you want to succeed on a Butsumetsu day. No weddings, no new product lines launched, no surgeries.
Taian (大安) These two characters mean the Big Safe. An auspicious day all around.
Shakko or shakku (赤口) Red mouth. The hours of the horse (11 am to 11pm) are good. Everything else, not so much.
In everyday life this calendar doesn't make too much of a fuss. But occasionally...
It is common for people to refuse being released from the hospital on a Butsumetsu. Instead they'll wait for a more favorable day to go home. Same with surgeries. I have relatives here who needed fairly immediate care but preferred to wait, again, for a more fortunate day before agreeing to the operation. Large construction projects (heck, even small ones) watch this calendar and will only start work on a Taian. I even read that when utilities companies want to change their rates they invariably do it on a Taian day.
Wedding halls charge different rates for different days. Even if the date is a Saturday in the Spring, if it happens to be a Butsumetsu the fee will be absurdly cheap; a Taian, absurdly expensive. No one wants to get married on an unlucky day, right? But recently younger folk who don't abide by the old calendar and traditions are taking advantage of these cheap rates and booking their weddings purposefully on the most unlucky day. Much to their grandparent's chagrin. My husband's cousin did this and it nearly drove his grandmother mad. She was beside herself and almost refused to attend the ceremony. In the end, she went but from that day on out any bad thing that happened to the couple was blamed on their choosing such an inauspicious wedding date.
This is the calendar the city prints out for all the residents.
See that writing to the right-hand side of the numbers? That tells you what kind of day it is. It is quite convenient. It also tells you when garbage days change and when the truck comes to pick up your used tempura oil!
My mother-in-law lives by this calendar and has one on hand at all times. For awhile I was a little gun shy when I mentioned anything that involved a date as she immediately looked it up and told me if I should proceed with my plans or not. Even having furniture delivered had to pass the Rokuyou test. Which super-sucked when our refrigerator broke and we desperately needed a new one but the nearest delivery date that passed her scrutiny was two weeks away.
It took awhile but now I'm used to it. On the plus side, if you know your Rokuyo you can really impress people. It's like a shoe-in to understanding the culture. Say you come across a group of old women chatting about the death of a neighbor. It is the middle of August (103-degree weather), so-n-so has just passed away and you realize the wake will fall on a Tomobiki (friend-pulling day). You automatically know that this means the family must keep the deceased in the house for an extra day. You also know that when the weather gets bad or changes suddenly a lot of the elderly pass away and the (one and only) crematorium gets booked up fast. Noticing the black and white signs all over the city announcing deaths in other households you assume that finding a free spot for the services will be difficult for the family. Your neighbors will most likely have to wait another day or two before the funeral. Add that houses here don't have central air and just your wince and the suggestion that it will be difficult for the family (everything is implied in Japanese) will bring knowing nods from the crowd.