Let me walk through the question in a condensed way.

1, 2, 3, 4, 5, 6, 7, 8, 9 (9 items)

1-9: 9 items (x1 group) (x1 digit each) = 9 total digits

10, 11, 12, 13, 14, 15, 16, 17, 18, 19 (10 items)

… 20s, 30s, 40s, 50s, 60s, 70s, 80s, 90s (8 more groups of 10 items each here)

10-99: 10 items x 9 groups x 2 digits = 180 digits

100, 101, 102, 103, 104, 105, 106, 107, 108, 109 (10 items)

… 110s, 120s, 130s, 140s, 150s, 160s, 170s, 180s, 190s (9 more groups of 10 items each here)

100-199: 10 items x 10 groups x 3 digits = 300 digits

We started by counting the single digits on their own, but we don’t count 0, so we only have 1-9 = 9 numbers.

Likewise, we count the double digits on their own, but since we’re not going 00, 01, 02, etc., we instead start at number 10, and then only have 9 groups (10s, 20s, … 90s).

The reason the triple-digit 100s has 10 groups is that we do have the 00s, i.e. 100, 101, 102…

So we have 10 groups (100s, 110s, …, 190s), since the 00s are our first group.

Hope this clears it up!