To solve this equation, we first need to convert the mixed numbers to improper fractions.

4 1/5 = (54 + 1)/5 = 21/5
1 1/5 = (51 + 1)/5 = 6/5
2 3/4 = (42 + 3)/4 = 11/4
1 7/18 = (181 + 7)/18 = 25/18

Now we can substitute these fractions back into the equation:

21/5 ÷ 6/5 = 11/4 * 4 - 25/18

Solving the fractions on the left side of the equation first:

21/5 ÷ 6/5 = (21/5) * (5/6) = 21/6 = 7/2

Now we have:

7/2 = 11/4 * 4 - 25/18

Next, simplify the multiplication on the right side:

11/4 * 4 = 11

Now we can replace the multiplication with their values:

7/2 = 11 - 25/18

To further solve the equation, we need to get a common denominator for 11 and 25/18:

7/2 = 198/18 - 25/18

Now subtract the fractions:

7/2 = 173/18

Finally, convert the improper fraction back into a mixed number:

7/2 = 8 7/18

So, the solution to the equation is 8 7/18.