First, simplify the numerator:

3lg 2 - lg 24
= lg (2^3) - lg 24
= lg 8 - lg 24
= lg (8/24)
= lg (1/3)

Now, simplify the denominator:

lg 3 + lg 27
= lg (3*27)
= lg 81
= 2

Now, divide the numerator by the denominator:

lg (1/3) / 2
= lg (1/3 * 1/100)
= lg (1/300)
≈ -2.5229

Therefore, (3lg 2 – lg 24) / (lg 3 + lg 27) is approximately -2.5229.