Answer
$h=0.4$
Work Step by Step
From the figure, the slope between $(0.7,f(0.7))$ and $(1.1, f(1.1))$ is given by
$$\frac{f(1.1)-f(0.7)}{1.1-0.7} = \frac{f(0.7+0.4)-f(0.7)}{0.4}$$
By comparing with $$\frac{f(0.7+h)-f(0.7)}{h}$$
we get $h=0.4$