To solve this equation, we first need to simplify both sides of the equation separately:

5 1/16 - 1 1/8 = 5+1/16 - 1+1/8 = 5 + 1/16 - 1 - 1/8 = 4 + 17/16 - 17/8 = 4 + (17*2 - 17)/16 = 4 + (34 - 17) / 16 = 4 + 17/16 = 4 1/16

5/6 + 3/14 = (57 + 36) / (6*14) = (35 + 18) / 84 = 53 / 84

Now, we can multiply the simplified values:

(4 1/16) (53/84) = (65/16) (53/84) = (65 53) / (16 84) = 3445 / 1344

So, (5 1/16 - 1 1/8) * (5/6 + 3/14) = 3445 / 1344.