Does Jordan recognize Palestine ?
Apart from the out of context quote of King Hussein bin Talal used by Mr. Davison in his answer, this was and is still used by Jordanians to sympathise and show solidarity with the Palestinian people. A basic knowledge of the Arabic language would make it clear, but propaganda has its purpose in the Israeli discourse.
As for your question, On 31 July 1988, Jordan recognized Palestine and renounced its claims to the West Bank (with the exception of guardianship over the Muslim and Christian holy sites in Jerusalem for protection), and recognized the Palestine Liberation Organization as "the sole legitimate representative of the Palestinian people."