Solution - Base conversion

$${\left(8A6\right)}_{16}$$

Expand digits with place-value powers in the source base.

$$8\cdot {16}^2+10\cdot {16}^1+6\cdot {16}^0$$

Sum the expanded terms to obtain the base-10 value.

$$2214$$

Expand each digit by place value: $$8·{16}^2$$
+ $$10·{16}^1$$
+ $$6·{16}^0$$. This gives $$2,214$$ in base 10.

$$2214\left(base10\right)$$

Use repeated division by the target base.

$$\frac{2214}{10}$$

Record quotient and remainder for this division cycle.

$$2214=10\cdot 221+4$$

Record quotient and remainder for this division cycle.

$$221=10\cdot 22+1$$

Record quotient and remainder for this division cycle.

$$22=10\cdot 2+2$$

Record quotient and remainder for this division cycle.

$$2=10\cdot 0+2$$

Read remainders from last to first to form target-base digits.

$$2214$$

Final converted representation in the target base.

$${\left(2214\right)}_{10}$$

Repeatedly divide $$2,214$$ by $$10$$, collect remainders, and read them in reverse to get $$2,214$$.