I am working on a document in italian and japanese.
For the japanese I use the font "MS Gothic" and everythig is ok.
The problem is with the pdf: some people see the japanese letters, some others don't.
So i decided to send the font to those who couldn't see them,
but the font (that I use every day) is nowhere on my computer...
You should pick another Japanese font that allows embedding in the PDF (though my version does say it has editable embedding permissions). I would also say that it might be a problem with the PDF viewer some people are using, They are not all created equal -- only Adobe Acrobat and Adobe Reader are guaranteed to fully support all PDF features.
As to why you cannot find the font, how are you searching? What OS? It's also a license violation for you to distribute the font directly...
Bear in mind MS Gothic is a licensed font, you do not have the rights to share it.
People who want to view PDF files with Japanese will need the Japanese version of Reader or to download a font package. Reader will say it needs a font package, but it's possible people did not mention this error.