i am assuming sinhx is hyperbolic sine of x.

sinhx = (e^x - e^-x) / 2

using series of e^x and e^-x and neglecting higher terms since x tends to 0.

(sinhx)² = {(1 + x + x²/2) - (1 - x + x²/2)}² / 4 = x²

so limit becomes

arrange it and use the series of sinx, you'll get 1/3.

 edited : Thanks allamraju, I did a slight calculation mistake. The answer is 2/3.