The given language is deterministic as we can see from the PDA shown below.
Here for any given input string, for each element of string we will push the items in the stack until we encounter $c$ ,after $c$ occurs we will pop the items from the stack until all the input string elements are processed.
If the Stack becomes empty at last(after processing the string) then we go to the final state and accept the input string.
Here the automata is deterministic because we know when we need to start popping from the stack.
