Seeing that there are 248 mitzvos aseh positive and 365 mitzvos lo taaseh negative, I heard someone note both add together to give 14: 3-6-5:14 and 2-4-8: 14. Is there a connection between that number and the two aspects of mitzvos?
I do not know of any source on this. But I was inspired by the OP to give this answer B"H.
14 in Hebrew is the value of the word "Yad". (hand) יד.
14 in Hebrew is the value of the word Yad backwards which is "Dye" (enough) די.
When we encounter a situation which the Torah tells us is forbidden, we limit our actions ("enough!") and avoid it.
When we encounter an opportunity to use a situation the Torah permits for a positive purpose, we increase our action to accomplish it. The "hand" symbolizes the power of action.
3-6-5 tells us that even if we start at 3 and increase our action to accomplish 6, sometimes we have to take a step back when encountering the forbidden - 5.
2-4-8 tells us, that when there is nothing forbidden, we can grow without limits and 2 becomes four and then 4 becomes 8 etc. :)
May we go from strength to strength in permitted ways according to the Torah.