Refer to figures.
There are two primary ways to mix air and fuel together in the right mixture, to be fed into the engine's cylinders. The first is the "old way", used in older cars and still many light piston aircraft, the carburettor. A carburettor uses a venturi to reduce the pressure of the air flowing into the engine air manifold, and this low pressure provides suction onto a fuel line which allows fuel to flow out into the airstream. It is, of course, more complex than this, but this covers the basics.

The newer method is "fuel injection". This is as it sounds, where, just before the fuel is introduced into the cylinders, the fuel injectors (very high pressure pumps) will provide an exact quantity of fuel, sprayed into the air, which atomises almost immediately to properly create the best mixture for burning inside the cylinder. In some engines (diesels in particular), this happens inside each cylinder separately, whereas some engines do it in the intake manifold.

As for the advantages of fuel injection over carburettors:

Advantages

• Very precise mixture control - the carburettor is not as precise in its mixture control and this also changes with ambient air pressure and speed, making it less efficient and more difficult to control.
• No risk of carburettor icing - "carb icing" is a large threat when using carburettors, as the venturi effect and the vaporisation of fuel both decrease the temperature of the air and this can quite easily lead to build-ups of ice in the lines and on the butterfly valve, leading to a rough-running engine and engine cut-out. Fuel injected engines do not have this problem, though can still suffer from intake icing (though much less likely), so most will have an alternate air source available.
• Much easier cold starting - Carburetted engines can be really hard to start when cold due to the mechanism which mixes the fuel and air, so you can quite easily flood the engine, etc., if you are not careful. Fuel injected engines are much easier to start in the cold.

Disadvantages

• More complex hot-start - Fuel injector lines can "vapour lock" if the engine is warm (has recently been running), so there is some fuel in gas form within the lines, which makes a hot start more complex as sometimes the fuel injectors are firing gas (completely wrong mixture) instead of liquid fuel. This makes following a hot-start procedure very important. Carburetted engines are much easier to hot-start.
• More complexity, possibly requiring backup pump type - Carburettors are very reliable and do not require any pumps or electricity to run correctly, but fuel injectors need pump pressure (engine driven or electrical) and timing, so are much more complicated, and therefore prone to failure in certain cases.

Therefore, going through the options:

• "Fuel injection provides better fuel management and fuel distribution to the engine."
  • CORRECT --> Fuel injection does provide better, more precise, fuel management and fuel distribution, whereas carburetted designs are more basic and rely a bit more on the conditions.
• "Vapour locks during ground operations on hot days are less likely to occur with fuel injection."
  • INCORRECT --> This is the opposite way round, fuel injection is more likely to have vapour locks on hot days (or hot-starts).
• "A disadvantage of fuel injection is the difficulty experienced in cold weather starting."
  • ​​​​​​​​​​​​​​INCORRECT --> Again, the opposite way round, carburetted engines are harder to start in cold weather.
• "Slow throttle response is one of the disadvantages of fuel injection."
  • ​​​​​​​​​​​​​​INCORRECT --> Throttle responses are almost instantaneous with fuel injection, unlike carburettors which can have some lag in certain conditions.