To solve this problem, we need to perform the given operations in the correct order.

First, let's divide 87m 23dm by 2:
87m 23dm ÷ 2 = 43m 11.5dm

Next, let's subtract 9m 8dm 7cm from the result:
43m 11.5dm - 9m 8dm 7cm = 34m 3.5dm - 9m 8dm 7cm = 25m - 1dm 7cm = 24m 9cm

Now, let's divide 90dm 30cm by 10:
90dm 30cm ÷ 10 = 9dm 3cm

Next, let's subtract 19dm 8cm from the result:
9dm 3cm - 19dm 8cm = -10dm - 5cm = -11dm 5cm

Now, let's divide 36m 8dm 7cm by 3:
36m 8dm 7cm ÷ 3 = 12m 2.8dm 2.3cm

Finally, let's subtract 12m 2.8dm 2.3cm from the result:
24m 9cm - 12m 2.8dm 2.3cm = 12m 6.2dm 7.7cm

Therefore, the final result is 12m 6.2dm 7.7cm.