Normally, a note is included with the power supply identifying the polarity according to ribs or stripes on the wires. Any illustration on the back of the part is probably only for the connector on the end of the part, but since the instructions are to cut the wires at the connector and strip and solder them direct, they must be identified using a tester, or, an LED and resistor.
The ends of the wires are comparable to a 12v AA battery pack, so you don't have to worry about getting shocked, but do take care to not let the two wires touch each other when their ends are stripped and exposed so as to not cause damage to the supply. A tester with a digital readout will show the dc polarity--if it's negative there will be a minus before the digits, if it's positive the minus will not be there. When the black probe is on the minus pole of the power supply and the red probe is on the plus pole of the power supply the dc reading is positive. With the red on minus and the black on plus, the reading will be negative with a minus symbol.
A tester with a meter that has a needle that swings across a scale would try to move to the left of the, at-rest 0v setting if the probes touch the supply with reverse polarity, so for this type, set the voltage range much higher than the anticipated 12v reading, say 100v or more, so if the probes are touched to the supply reversed, then the needle will only slightly move one way or the other. Movement to the left means the black is on the plus pole and the red is on the minus pole. Movement to the right means the black is on minus and the red is on plus.
An LED and resistor (1000 to 4700 ohms (1k to 4.7k)) will show the polarity of the supply too. The LED short leg nearest the flat edge is the minus end. Hold it against one of the two supply wires and hold the resistor against the other supply wire. Touch free end of the resistor to the free end of the LED and if it lights, the LED is touching the minus pole of the supply. If it doesn't light, swap the wires and it should.
Note any stripe or ribs on the wire and make a note of which is the minus pole and the plus pole of this dc power supply.
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