If the slopes of the two lines are m1 and m2, the angle θ is obtained from

tanθ =∣(m1−m2)/ (1+m1m2)∣

lets write the equations on the lines in standard form and determine the slopes

3x-4y=8 in standard form is y = 0.75x - 2 thus the slope is m1 = 0.75

x+2y=4 in standard for is y = -0.5x + 2 thus the slope is m2 = - 0.5

click here to see the graph and conversion the standard form

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now we have

tanθ = ∣(0.75 - (-0.5))/ (1+ 0.75(-0.5)∣

tanθ = 2

θ = arctan 2

θ = 63.43 degrees is the acute angle between the lines 3x-4y=8 and x+2y=4.