Egg bread recipe calls for 2 eggs and 2 yolks, can I use 4 whole eggs?
Let's put it this way - you can, but there will be consequences, so you probably shouldn't.
Bread dough that behaves like you expect it to depends on a given amount of liquid for a given amount of flour. Using whole eggs instead of just the yolks called for increases the liquid, so you'll have a runnier dough while its raw, making it harder to knead, so then you're tempted to add more flour and everything gets out of whack.
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In bread making, an egg is a liquid. One egg yolk is about 20 grams of liquid. One egg white is about 40 grams.
So four eggs are 460=240 grams or milliliters (a bit more than a cup of liquid), while two eggs and two yolks are 260=120 grams plus 2*20=40 grams for 160 grams of liquid (a bit less than 3/4 of a cup).
So what to do with the leftover egg white? There were good suggestions here already, but I like to either freeze it for later use, or stir it with something flavorful (anchovy, parmesan, garlic, and then fry it up and eat it now or chopped in a salad later :)