Let me try it.

2.2 pounds in a kilogram, so one pound is 1/2.2 kilogram, i.e. 10/22 kilogram.
1/18 and 10/22, change the denominator to both: 1/18 to 11/198, 10/22 to 90/198.
Then 90/11 is about 8. So there are 8 of 1/18 kilogram in a pound.

8 is the answer.

Great work, Gissinggy! You beat me to it...I was halfway through my explanation and saw that you already had it!

As a teaching tool, let me point out the importance of conversion factors (or "dimensional analysis"). Units will cancel the same way that factors will if you multiply/divide them, and knowing that can help you out immensely. My favorite example of this is a question I ask my students all the time:

If you're driving 60 miles per hour, how fast is that in miles per second?

And almost everyone knows you have to either multiply by 60 twice or divide by 60 twice to account for the fact that there are 60 minutes/hour and 60 seconds/minute. But they're about 50/50 on which one it is, and those who decide to multiply end up with 216,000 miles per second - faster than the speed of light! What's funnier is that I've even had students argue with me that they're right - that on their way home from class they'll actually travel back in time somehow because 'well, that's what the math says...'.

Dimensional analysis says that if I have miles/hour and I need to get to miles/second, I need to take the 60 minutes : 1 hour and 60 seconds : 1 minute ratios and get the units to cancel out so that I get from hours in the denominator to seconds. So I have:

miles/hour * hours/minutes (so hours cancel) * minutes/second (so minutes cancel, and I'm left with seconds in the denominator:

60 miles/hour * 1 hour/60 minutes * 1 minute/60 seconds ---> 1/60 miles/second.

So in this problem, we have 1 pound, and we have the ratios:

2.2 pounds : 1 kg
18 eighteenths-of-a-kilogram : 1 kg

We want to get from pounds to eighteenths-of-a-kg, so we'll set up the math:

1 pound * 1kg/2.2 pounds (so pounds cancel) * 18 eighteenths/1kg (so kgs cancel and we're left with eighteenths):

1 * 10/22 * 18/1

And then we can simplify the math using fractions:

180/22
90/11
88/11 would be 8, so this is just over 8 as Gissinggy says, so the answer here is 8.