#mana reflection

Quick answer: You get your choice of one or two colorless mana. (Or four colorless mana if the land naturally produces two or more mana.)

Long answer: When you tap your land for mana, you’ll first check to see which replacement effects want to apply to that ability. If the mana ability you’re using only normally produces one mana, then Damping Sphere won’t apply yet and you just apply one of the Mana Reflection effects and double the mana that would be produced. At this point, both Damping Sphere and the other Mana Reflection want to apply their effects, so you choose which of them to apply next. If you apply Mana Reflection again here, then you’ll double the mana again but have to apply Damping Sphere at the end, which reduces your final output to one colorless mana. If you apply Damping Sphere first, then you get knocked down to one colorless mana, but the other Mana Reflection then doubles that to two colorless mana. If the mana ability you’re using naturally produces more than one mana, then you can apply the effects in any order to get one, two, or four colorless mana, depending on when you apply Damping Sphere’s effect.

When you tap your mountain for mana, it would normally produce R, but Mana Reflection’s replacement effect doubles that to RR. Dictate of Karametra then triggers and gives you another R when its trigger resolves. So you get RRR, but only two of the three mana is from the mountain.

In the case of a land that actually produces multiple colors of mana, say a Gruul Turf, it would tap for RG, which Mana Reflection doubles to RRGG, and the Dictate of Karametra triggers and gives you another R or G. So here you’ll end up with your choice of either RRRGG or RRGGG.

No.

If you tap your Forest Swamp for green mana, you’ll get BGG. The mana produced by Crypt Ghast’s ability is produced by its triggered ability, not by you tapping the Forest for mana and thus Mana Reflection’s replacement effect doesn’t apply to it.

They don’t. They each just do their thing.

Mana Reflection is a replacement effect. It modifies how much mana is added to your pool each time any mana is added (assuming it came from tapping a permanent).

Doubling Cube’s ability is an activated ability. It doubles how much mana is currently in your pool at the specific time it is activated.

If you’re not sure what the difference is, check out:

MTG Tutorials #2: All About Activated Abilities

MTG Tutorials #24: All About Replacement Effects

While you’re at it, you also might want to check out:

MTG Tutorials: Extra Credit — All About Mana

Up to speed? Good. 

Here’s an example of how these two cards play together:

Say you control Mana Reflection, six Forests, and Doubling Cube. You tap all six Forests to add 6 green mana to your mana pool, but Mana Reflection’s replacement effect doubles that 6 mana to 12. Then you spend 3 mana (putting you down to 9 in your pool) to activate Doubling Cube’s ability. 

When that resolves, Doubling Cube sees you have 9 green mana in your pool currently, and tries to double it by adding 9 more — but wait! Mana Reflection sees you trying to add mana to your pool again, and doubles the amount being added. Because of Mana Reflection, the 9 mana from Doubling Cube becomes 18, which gets added to the 9 you already had.

In the end, you’ll have 27 green mana floating in your mana pool — not bad considering it all started with six measly Forests.