How do I deal with Enchantments while playing mono-red?
There are a few artifact answers to Enchantments in standard. Red will have access to those dealing with permanents, which are going to be slower. However, there are "ramp" cards in Standard for red that help you get them out more quickly.

Ratchet Bomb, can come out quickly, but takes time to "charge up" to the point where it can deal with more expensive enchantments. Although slow, it also deals with other permanents (eg. planeswalkers). If you get it out before the enchantment or planeswalker and charge it up, it can be a threat on the board causing your opponent to think twice before casting.

If you can ramp into a Spine of Ish Sah, say with a Geosurge on turn 4, you will be well on your way to victory, and getting rid of that pesky enchantment.

However, I think the most efficient way to deal with enchantments in standard, if you insist on mono-red, is to use the Sylvok Replica, and access green mana through dual lands  and/or a colourless ramp like Alloy Myr, Manalith or even Sphere of the Suns that also helps you power your X burn spells and getting bigger threats out more quickly.

But at that point you may as well just splash green dual lands or ramps and put Naturalize on the sideboard.

In Legacy, if it's Blue enchantments you're concerned about, Jaya Ballard, Task Mage is a great choice. Aura Barbs punishes those who dare use enchantments against you. Of course, Larry Niven's Disk has been the go-to solution for red burn decks since forever.

PS. I don't agree with this:


  Red must be fast and win before enchantments are out" is not a good solution, because in the example above the enchantment can hit in round 2.


Meh, CoP:Red isn't in Standard anymore, and even in Legacy the opponent is unlikely to have enough mana to deal with all your threats if you have a red weenie swarm, or save some of that red magic for when he's tapped out. You also have colourless options.

Red decks still win because they're fast. They generally aren't afraid of many enchantments.