How to prove Halting problem is solvable by oracle machine
An oracle machine is a regular machine, such as a Turing machine, with an attached device that is an oracle.  This oracle, often called a black box to signify that it is not constructible in the real world, answers questions about some set. 

For instance if the oracle is a $K$ oracle then it can answer yes or no whether numbers are in the set $K$ (I'm taking $K$ to be the name of the set of natural numbers $e$ such that Turing machine $e$ halts on input $e$).  So obviously the Halting Problem can be solved by a machine that has access to this oracle.