The through-hole one looks perfect. Thank you
Update:
I got some new transistors and they seem to be working. However, I believe that when current is sent through the solenoids, there is not enough resistance, so it results in a short. For example, when I activate two or more solenoids at any given time, the DC adapter shuts off to protect itself. What can I do here? The resistors I see at Radio Shack can handle a max of 1Watt power. I'm running 1.8 Amps and 16.6 Volts through the solenoids, which have impedance of 12 Ohms.
Simply get a bigger power supply, one that can give more current.
There are 3 voltages commonly quoted in the specs. One is in the "Absolute Maximum Ratings" section, that's the absolute maximum Vgs (gate-source voltage) - this is usually something like +/-20V. If you take the gate source voltage that high then the gate oxide may breakdown (device dies).
There is the VT - the FET threshold gate voltage. This varies a lot between devices, so is often quoted as loosely as "2--4V". This is the point at which the device starts to conduct (usually a few microamps is the criterion). Below this the device is OFF.
Then there is the Rds(on) specification, something like "Rds(on) = 0.004 ohms at Vgs=4.5V" - the Vgs specified here is the gate voltage for the FET swiched fully on. Typically the Vgs quoted is 10V or 4.5V (for logic devices). Some devices quote both (the on resistance is less at 10V gate drive of course, but only a little less since the device is basically fully ON at 4.5V). 4.5V is quoted rather than 5.0V to allow for the device that drives the gate not being able to pull fully up to the rail. If the spec is for 10V this is usually taken to mean "use 12V of drive".
This "Rds(on)" is the important section, its saying what voltage you need to drive the gate to get the device turned on (and how low a Rds resistance there will then be guaranteed). You should probably check the absolute maximum as well of course, but you can ignore VT
If you take Vgs to somewhere between VT and the quoted Vgs you'll half-switch-on the device - since VT is highly variable you cannot be sure how well the device is turned on - you are in the linear region rather than the switching regime.