Alright, let's walk through the math.
Spike has 2 phyrexian mana symbols in her casting cost. Each one costs two life, so paying life for both will cost 4 life, and then two generic mana to cast Spike.
Her ability has 4 phyrexian mana symbols. Because each one cost two life, the total cost for activating her ability is 8 life.
Now let's walk through this. Casting Spike will cost 4 life. If you activate her ability once, you will have lost 12 life total. Activate it again, and you have lost 20 life so far. Activate a third time, and that makes 28 life. After a fourth time, you will have lost a total of 36 life, leaving you with 4 life left.