I have both good news and bad news for you here. If you want the short answer:
it MIGHT likely run... But it's a risk. (on an aside, the reliability of this answer partly hinges on your CPU: you forgot to list what it draws as well!)
To go into more detail... The GTX 660 has a tdp of 140 watts. As with any GPU, the bulk of that comes in the form of +12v... That means that the card is going to use up approximately 12 amps of +12v. So from this standpoint, yes, it's well within the old-standard "safety limit" of no more than 18 amps or so of +12v per output. However, it's a bit more complicated than that.
You might recall that a 6-pin PCI-e connector only provides up to 75 watts of power: up to 3.125 amps each on two +12v wires. (yellow, if they follow the standard coloring) So at the very least, 65 watts are going to be drawn from the PCI-e slot (which has a cap of 75W on its own) The PCI-e slots are powered through the MOTHERBOARD's PSU connector (that big 24-pin block) so already, the GPU's being powered through two different lines... And generally, those two lines are split on two separate rails: the first +12v rail tends to include the motherboard and CPU (the extra 4/8-pin conectors that go to the motherboard near the CPU) while the second covers all "peripheral/card" plugs: the PCI-e conector, the SATA plugs, and any 4-pin Molex plugs. So good news there:
you shouldn't have to worry about what rails are going where.
However, then we have to look at the power supply itself. I'm certain that by now you've gotten plenty of comments that it's junk, based on the name alone; PSU enthusiasts tend to (for often good reason) gain great suspicion of any brand name they don't immediately recognizing, falling back on a handful of core names like Seasonic, Corsair, and Silverstone. However, if we look up the brands involved... We see that
Powerman's PSUs are actually made by FSP, which is a KNOWN maker of decent power supplies... While not a true A+ tier like the aforementioned brands, they are known to provide a number of units that are comparatively solid and suitable for even midrange enthusiast PCs. However, if we go by the UL number,
we get a weird, conflicting story; it lists "In Win" as the OEM, though since we known In Win just labels them, it means we're not entirely sure of its origin.
FURTHERMORE, if we
I can't seem to find that model anywhere on the page; it may have actually NOT been certified by the UL. In fact, the closest I could find to it was the "IP-S450BQy-z" though that lists its only input range as 200-230v.
Additionally, we know that the unit you have is definitely not one of the better ones: one giveaway is the red input voltage selector in the back, which implies the unit has a passive PFC rather than an active PFC; as a result the unit would be less reliable when put under a heavy load... And a heavy load is what you'd be subjecting it to: ideal PSU loading is to not go over 50% of its total wattage capacity. With 140 watts already down for the PSU, you'd leave the rest only 85 watts total before you passed the 50% mark of 225w. Chances are pretty solid you'd go past that; the CPU alone could easily use more than such.
And in such a case where you load it heavily, it could be dangerous: most *GOOD* PSUs only claim their maximum wattage is equal to whatever it can provide in +12v alone, which is a clear indication of conservative ratings... Meanwhile this unit clearly doesn't do that, listing only 360w/450w for +12v. Furthermore, "18a" is just the standard boilerplate rating given, as older standards dictated that be the cap for any +12v rail.
All of this boils down to
a PSU that may have been of good manufacture, but isn't entirely of known make, and appears to have an over-rated wattage. So while it might've been made by FSP, it could've been one of their poorer units, and more than likely wasn't rated by FSP for 450w, instead perhaps a 350-400w unit. So while
I'm pretty confident your card would run, expect it to burn up the PSU abnormally fast. When the PSU starts failing, you could run the risk of it damaging the circuits of your other parts.