"I do not know the color of your jacket."
Translation:Non so il colore della tua giacca.
Sapere is to know things or information. Conoscere is the verb to know about any person or place. For instance, to say I know the color, io so il colore. To say I know the woman, you say io conosco la donna. Everything that's not a person or a place, use sapere otherwise use conoscere!
i think 'io so' (sapere) means that you know something, because you learnt it. 'io conosco' (conoscere) means you know something, because you have met with it (it also means 'meet') 'io so' is more general. At least that's what i learnt about it, i hope somebody will complete it with more examples.
I think sapere is to literally know something and conoscere is to be acquainted or familiar with something. Such as, one can be familiar with a street in the sense that you know where it leads and what can be found by that street, but in many languages it's not really "knowing" the street, you are just familiar with it. Same with people. You are familiar with a person because you have talked to him/her, but this to Italians doesn't constitute as "knowing." A whole lot of languages make the difference, so it's just something to get used to. You use sapere when you can actually know something by making observations about it, generally speaking. You see someone's jacket is yellow, so you SAPERE that the jacket is yellow. If you have seen someone wear that jacket before, you can shout "I CONOSCERE that jacket!" (I know/am familiar with that jacket.)
Long story short; sapere = to know a piece of information conoscere = to be familiar with an object (restaurant, street, person)
This is only how I understand it, please correct me if there is something that needs correcting.
To do the possessive (your jacket), it would be "la tua giacca" (feminine). Since it is the color "of" (di), you have to combine the "di" with the "la" from the possessive part. "di" + "la" = "della". That leaves you with "della tua giacca" (not "dila" tua giacca, or just "di" tua giacca).
If the object was masculine, say a hat, then your hat is "il tuo cappello", and the color of (di) your hat is "di" + "il" = "del", so it would be "del tuo cappello".
Here is a very good link for you (the "di + article" is the second chart from the top): http://www.angelfire.com/ky/LeCorde/italiano.html
Conoscere is when you're familiar with something. Most often, that's people and places, but in this instance, it's more like "I'm not familiar with the color of the jacket" like you don't know what to call the color of the jacket. Sapere technically could be used, but conoscere is correct too.
The "lo" refers to what you do not know, as in "it" ...."I do not know it". If they asked you the color of the jacket and you want to say only that you do not know, then you use "Non lo so". But since you are actually saying "I do not know the color of the jacket", then the "the color of the jacket" takes the place of "lo".