The correct spelling of the phrase "backing salt mines" is as follows: /ˈbækɪŋ sɔlt maɪnz/. The word "backing" is pronounced with a short "a" sound, as in "bat", followed by the "-ing" suffix. "Salt" is pronounced with a short "a" sound as well, and the "l" is not silent. "Mines" is pronounced with a long "i" sound, as in "eye", followed by a silent "e". This phrase refers to the financial support or investment made in salt mines.