David,

For a two digit number in base ten the leftmost digit is the tens digit and the rightmost digit is the units digit. Thus 43 is 4 tens and 3 units. For a two digit number in base b the leftmost digit is the b digit and the rightmost digit is the units digit. Thus 43_b is 4 bs and 3 units. So if b is 8 then 43₈ is 4 eights and 3 units, that is thirty-two plus three which is thirty-five.

This means that 10_b is one b and zero units. Thus the value of 10_b is the value of the base b. Hence if b = 8 as above then 10₈ is eight.

Hence in your question above 10_b is the value of the base, 11_b is the value of the base, plus one and 12_b is the value of the base, plus 2. So if the base is 8 then 10₈ is eight, 11₈ is nine and 12₈ is ten.

I hope this helps,
Penny