Now I know Grandpa asks silly questions all the time.
He says to me:
"Son, this is based on my personal experience.
I was with a friend today. He made a gesture. By making this gesture he showed me that 3 can mean 6."
What gesture did Grandpa's friend make?
Well this is a bit far fetched but let's try:
Three pregnant women, each carrying one child equal six people. :)
The Answer could be
The Roman Number III = VI With the First two lines joined together at the bottom?
Guess,
If three is a crowd, six could be a crowd too.
And
If grandpa was talking about having guests somewhere and if you have three guests it is a crowd, and if you have 6 it is also a crowd.
Perhaps
Grandpa and his friend return home after a long night at the bar. "Look grandpa," his friend says, holding up 3 fingers. "How many fingers am I holding up?" Even though the world spins around in circles, grandpa manages to focus his eyes on his friend's hand. The fingers blur and seem to split in two. "6," he breathes. "6 fingers."
Not completely "non-math", but the crux of my solution is linguistic:
3 (numbers) can mean (average to) 6, e.g. the three numbers 4, 5, 9.
$$3!=6.$$
The story of three is $6$
so...
...the answer will be six with the help of using $3$ only.
Some users here might find this answer sexist, but unfortunately, it is true.
In some countries, the legal status of a woman is worth half of that of a man.
So, my guess is
The testimony of six women equals to three men.
The gesture Grandpa's friend made was the sign for the number 6 in American Sign Language.
The sign consists of pointing your three middle fingers up while connecting your pinky and thumb, palm facing forwards. A picture of it can be found here.
Thus,
3 fingers = 6.
This fits the question because:
Apart from being language and gesture related, it does not involve math, and a previous question has indicated Grandpa lives in the U.S.
How about:
When $$a(3)=6$$ According to OEIS, this is over $180,000$ results. In English, we would say, 'when is a(3) equal to 6', but if you were a big OEIS fan, and you know all sequences use 'a' terms, so you drop the sentence's reference to 'a' - 'when is 3 equal to 6?' is what you might say.
Could he mean this?
The “one, two, many” theory is that cultures developed words for “one” and “two” before anything else, and any numbers after are referred to as “many”. So three could be equal to six.
This answer is "language related".
Grandpa and his friend were out clubbing tonight (grandpas can go clubbing too!). The friend went to get some drinks. Seeing the queue at the bar, he thought he could order all drinks of the night in one order so he would't have to queue again. So he turns to the grandpa, trying to ask him how many he wants. But grandpa doesn't understand him, since the music is too loud and grandpa's hearing could be a bit better anyway. So what the friend does is achieve eye contact with grandpa and hold up three fingers, mouthing the word "three drinks?". Grandpa is a little confused by that number and just agrees, nods, and puts one thumb up. He thinks maybe his friend picked someone up already and that would be why the friend wanted to get three drinks. But what the friend was actually asking if grandpa also wants 3 drinks for the whole night. So when grandpa affirmed "three", the friend went ahead and bought six. 3 = 6. QED.
The gesture mentioned in the edit is of course the showing of the three fingers. Oh how close to the solution I was with that gesture. I drafted this while gestures were not mentioned yet in the question
