You won't be able to get to 6000 calories overnight, nor will you need to. You likely won't be able to stand an increase of more than 500 daily calories per week. So, work up in increments.
It will be a real challenge to get enough calories, but it's more important to make sure that you're getting those calories from protein. I mean, think of it this way... calories are kind of overall important, but macronutrients are most important. If you get your macronutrients right, especially the protein, the calories will fall into place--but not necessarily the other way around. Macronutrients, as you may know, are the types of nutrient calories you can consume. The important ones are carbohydrates, protein, and fats.
For instance, if you're getting 1 gram of protein per pound of bodyweight (or some even say per pound of target bodyweight, i.e. what you want your weight to be), that should be roughly 30% of your calories. Whether you're under or overweight, this protein is important. If you're overweight, it's even more important, and protein may make up as much as 40%+ of your macronutrient ratio. Protein has 4 calories per gram, so...
180lbs = 180 grams of protein = 720 calories
220lbs = 210 grams of protein = 840 calories
260lbs = 260 grams of protein = 1040 calories
etc.
Then, when you're bulking, go for about twice that amount in carbohydrates. If you're trying to do a "clean bulk," where you may not have as much energy and gains but will gain less fat, you can bump it down so that you're only getting 50-55% of your calories from carbohydrates. Or, if you're trying to cut or lose weight, you'll only have about 40-45% of your calories from carbs. So adjust carbs accordingly.
Examples:
A 160lb person, trying to get to 180lbs+ while gaining muscle might consume 180 grams of protein and 340 grams of carbohydrates per day.
A 220lb person, trying to stay in the 200-240lbs range while gaining muscle and losing fat might consume 240 grams of protein and 380 grams of carbohydrates per day.
A 260lb person, trying to lose fat and maintain or gain muscle might consume 260-300 grams of protein per day and 300-340 grams of carbohydrates per day.
It is important to be discretionary in your consumption of carbohydrates, though. Realize your body uses these for energy, and consuming simple carbs, especially refined sugars, are not going to be ideal because it will be too much energy at once, and your body will store it or be degraded in processing them; too simple of carbohydrates causes an insulin spike, which is almost always bad. The exception is after you've worked out and your muscles are starving for nutrition... this is why a Gatorade (powder-based, not bottled) or one of those NoXplode drinks along with 40-50g of protein is a great idea within an hour of working out. Insulin enhances nutrient, energy, and creatine reuptake in your muscles. (Also, since I don't know how much many here know about creatine, NO, it is not a steroid or anything like that, it is a substance your body naturally produces in moderate amounts when you have 110% correct nutrition. Supplementing it is totally natural and healthy.)
Fats are best to avoid, but make sure you get your healthy fats. You'll probably get enough from just consuming normal meats, like chicken, fish, beef, as well as dairy products like milk, and such. Many take their "healthy fats" or EFAs (Essential Fatty Acids) daily in the form of fish or flax oil caplets. I recommend flax oil caplets, because they don't taste NEARLY as bad as fish ones.. big mistake srsly). You could also *eat* crushed flax seeds or take tablespoons of the oil daily.. but again, I don't recommend it.
You specifically, BiTurbo, will have to eat everything and the kitchen sink... instead of Muscle Milk type stuff (a really lean protein shake), look for full "Meal Replacement Powders" or shakes, and meal replacement bars, such as MetRx's Big 100 bars. You need all of the cals you can get. Obvious stuff also applies, like pre-packing your lunches, a variety of RTD (Ready To Drink) solutions for when you forget, and breaking your calories out into as many smaller meals per day as you can handle. 6 or 7 is totally doable, including both pre- and post-workout meals. Eat as soon as you wake up and right before you go to sleep... your body needs all of the nutrients it can get.