confusion regarding elasticity of a demand curve

It is correct that the higher the elasticity is the more flat the demand curve will be. A higher elasticity means that demand responds disproportionately more to change in prices. In fact an example of demand curve where elasticity $ | epsilon| = infty$ would be a flat horizontal demand curve.

The reason for this is that elasticity of demand tells you how much quantity demanded (plotted by convention on x-axis) changes in response to change in price (by convention plotted on y-axis). In order for a small price change (small distance 'traveled' across y-axis) to have large impact on quantity (distance 'traveled' across x-axis) the curve has to be relatively 'flat' since the slope which will be the rise/run of tangent line at a given point must be relatively small.

For example if elasticity $| epsilon | = 2$ that means that $1%$ decrease in price increases quantity demanded by $2%$. Since total revenue is defined as price times quantity $P*Q$ if $P$ decreases only by $1%$ but $Q$ increases by $2%$ the total revenue has to increase. So the answer provided is correct.

To actually showcase how the demand becomes more 'flat' I generated 3 constant elasticity of demand functions ($P=Q^{1/epsilon}$) using R for natural numbers $Q = 1, ..., 10$. The blue demand curve has constant elasticity of $0.5$, the orange one $2$ and the red one has constant elasticity of $5$ (all expressed in absolute value). You see as the elasticity increases the demand graph becomes more 'flat'.