Binomial Option Pricing:

Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $46.00, = 0.28, r = 0.06 and the dividend yield is 2.0%. What is the maximum approximate strike price where early exercise would occur with an American call option?

According to my professor, the answer is 19.26. His explanation:

We need to solve for K in the following inequality

max(Su-K, 0) e^(-r*h)*(p* max(Suu-K, 0) + (1 - p*)max(Sud - K))

Can you explain how to solve that and to arrive at the answer of 19.26? Thanks!