Refer to figures.
Density altitude is a concept used in aviation and meteorology to describe the altitude at which an aircraft "feels" like it is flying, taking into account the effects of temperature and humidity on air density. It is not a physical altitude but rather a theoretical one that helps pilots and meteorologists assess aircraft performance and weather conditions.

Air density is affected by temperature, pressure, and humidity. As temperature and humidity increase, air density decreases, causing a decrease in aerodynamic lift and engine performance. Conversely, as pressure increases, air density increases, improving aircraft performance. Density altitude is the altitude in the International Standard Atmosphere (ISA) at which the current air density would be found, considering these factors.

The Maximum Take-Off Mass (MTOM) is the limited mass of the helicopter for take-off and can be affected by various factors due to performance of the helicopter, the conditions that affect MTOM are temperature, humidity and altitude.

To solve this question it’s necessary to be familiar with CAP 758, find figure 1.1 and figure 3.2 in the CAP 758.

1. In figure 1.1 we can derive the density altitude by finding -20^oC and 11 500 ft Pressure Altitude (PA) thereafter, find the intersection of the two lines and move to the left of the graph to find the Density Altitude (DA) of 10 000 ft.
2. In figure 3.2 find on the left side the DA of 10 000 ft thereafter, move to the right all the way to the end of the envelope in order to find the MTOM for this DA. Move down to find the MTOM given as 7 700 kg (17 000 lbs).