Can a 12V LiFePO4 battery be charged using a car battery?
If you just hook the LiFePo up to a car battery, you'll get a lot of smoke from both the cables and the batteries involved, and it can also cause the LiFePo to ignite or explode.
The problem is that there's nothing to limit the current flowing into the LiFePo battery. A car battery can easily provide thousands of amperes of short-circuit current, and if you connect a LiFePo across it, you have created just such a short-circuit. Assuming that your LiFePo battery is fully discharged, which means it has a cell voltage of 2 Volts, the total voltage of the battery will be at 8 Volts (4 cells in series). The car battery, on the other hand, might have 13 Volts when fully charged. That's a difference of 5 Volts, which will cause a massive current to flow that's only limited by the circuit's total resistance (which is mostly in the wires connecting the batteries). If we now assume that you've connected the batteries using 1 meter of 10AWG wire, this will give us about 3.3 Milliohms of total resistance. 5 Volts across 3.3 Milliohms results in a massive 1500 Ampere current flowing into the LiFePo battery, for a total power dissipation of 7500 Watts (1500 Ampere at 5 Volts cable drop). In practice, it'll be slightly lower due to the batteries' internal resistance, but it won't change the fact that things will blow up almost instantly. It also won't be any better if the LiFePo battery isn't fully discharged, it'll still dump thousands of Watts into the cables and burn them (and the batteries too).
Even if you managed to limit the current, you still need a balancer to properly charge a LiFePo battery, otherwise individual cells might get over-charged and damaged.
TL;DR: Don't do this, the batteries and cables will blow up. Always use a proper charger.