a bag has 5 red marbles, 6 blue marbles, and 4 black marbles.?

Each time you will have the same distribution of marbles, because you return the drawn marble.

The probability of picking blue is 6/15 (or 2/5)
The probability of picking black is 4/15

The probability of both events happening in that order is the product:
P(blue, then black) = 2/5 x 4/15 = 8/75

Answer:
8/75

[ 6/15 ] [ 4/15 ] = 24 / 225

Blue: 6/15
marble replaced
Black: 4/15
so
Blue AND Black = 6/15 * 4/15 = 24/225

Probability of Picking a blue marble 6 to 10
Probability of picking a black marble 4 to 11

6/15 x 4/15

6/15 x 4/15

blue then black

(with replacement)
(6/15)(4/15) = 24/225 ≈ ...107

(without replacement)
(6/15)(4/14) = 24/210 ≈ ...114

6/15 x 4/15

chance of getting a blue marble: 6/(5+6+4) = 6/15 = 2/5
chance of getting a black marble: 4/(5+6+4) = 4/15
answer: (2/5)*(4/15) = 8/75 =~ 0...1066666666666666666666666666666.........

6/15 X 4/15

Chance of getting a blue marble: 6/(5+6+4) = 6/15 = 2/5
Chance of getting a black marble: 4/(5+6+4) = 4/15
Answer: (2/5)*(4/15) = 8/75 =~ 0.1066666666666666666666666666666...

blue then black

(with replacement)
(6/15)(4/15) = 24/225 ≈ .107

(without replacement)
(6/15)(4/14) = 24/210 ≈ .114

Pr(Blue and Black)=Pr(Blue) x Pr(Black) = ...