  FRB 20180916B is a repeating fast radio burst (FRB) with an activity period
of 16.33 days. In previous observations ranging from $\sim 150-1400$ MHz, the
activity window was found to be frequency dependent, with lower frequency
bursts occurring later. In this work, we present the highest-frequency
detections of bursts from this FRB, using the 100-m Effelsberg Radio Telescope
at 4$-$8 GHz. We present the results from two observing campaigns. We performed
the first campaign over an entire activity period which resulted in no
detections. The second campaign was in an active window at 4$-$8 GHz which we
predicted from our modelling of chromaticity, resulting in eight burst
detections. The bursts were detected in a window of 1.35 days, 3.6 days
preceding the activity peak seen by CHIME, suggesting the chromaticity extends
to higher frequency. The detected bursts have narrower temporal widths and
larger spectral widths compared to lower frequencies. All of them have flat
polarization position angle sweeps and high polarization fractions. The bursts
also exhibit diffractive scintillation due to the Milky Way, following a
$f^{3.90\pm0.05}$ scaling, and vary significantly over time. We find that burst
rate across frequency scales as $f^{-2.6\pm0.2}$. Lastly, we examine
implications of the frequency dependency on the source models.
