Shift elements of array three places to left within java

Well, you need temporary storage of some description. If you have enough memory, you could do this in one go:

int[] buffer = new int[placesToShift];
// Save the start of the array in the buffer
System.arraycopy(array, 0, buffer, 0, placesToShift);
// Copy the rest of the array into place
System.arraycopy(array, placesToShift, array, 0, array.length - placesToShift);
// Copy the buffer into the end
System.arraycopy(buffer, 0, array, array.length - placesToShift, buffer.length);

It's also worth noting that you can always get by with at most half the array length as a buffer, by treating (say) a "shift left by 4" as a "shift right by 1".

You can do it with constant extra space by repeatedly shifting once. For example:

for (int i = 0; i < placesToShift; i++) {
    int firstElement = array[i];
    System.arraycopy(array, 1, array, 0, array.length - 1);
    array[array.length - 1] = firstElement;
}

That's inefficient in time of course, but efficient in space.