To simplify the expression \( 1.5(3x+4) + 0.25(6x+8) \), we first distribute the constants in front of the parentheses.
Starting with the first part, \( 1.5(3x + 4) \): \[ 1.5 \times 3x = 4.5x \] \[ 1.5 \times 4 = 6 \] So, \( 1.5(3x + 4) = 4.5x + 6 \).
Next, for the second part, \( 0.25(6x + 8) \): \[ 0.25 \times 6x = 1.5x \] \[ 0.25 \times 8 = 2 \] Thus, \( 0.25(6x + 8) = 1.5x + 2 \).
Now we can combine both results: \[ 4.5x + 6 + 1.5x + 2 \]
Next, we combine like terms: \[ (4.5x + 1.5x) + (6 + 2) = 6x + 8 \]
The simplified expression is: \[ \boxed{6x + 8} \]